Good question. I am answering more to brainstorm along with you than anything else. I think that you have the broad bases covered, but the finer details of implementation are important.
It is tough for a PhD program in mathematics to directly network with undergraduates, because being an undergraduate math major is almost entirely about coursework and very little about research. This limits the usefulness of one of @jakebeal's suggestions in this field: most undergraduates do not understand the research that faculty members are working on -- I mean, do not understand at all, including not knowing what most of the nouns are -- and this makes it difficult to promote faculty research to undergraduates. For instance my most durable research interest over the years has been the period-index problem in Weil-Chatelet groups of abelian varieties. This is a plausible topic for PhD research for a UGA student -- in fact, a student just last month received a PhD at UGA on this topic under my supervision -- but the undergraduates who have any clue what this means are not coming to UGA. So what can you do?
- Adjust your research program so that some part of it makes sense to some undergraduates.
When I was a postdoc, this would have sounded unlikely to me. As a postdoc I did supervise two undergraduate students' summer research (at my institution), and that research was on a problem in real analysis...which I chose because they were the grader and one of the students in an undergraduate real analysis course I had taught. When I arrived at my current good but not-too-elite tenure track job, I made it a point in my early years to acquire a much broader, shallower knowledge of my own subject (number theory) than I had as a student. Then over the years I have led two different research projects whose main goal, honestly, was to be pitched lower to the ground than WC groups or Shimura curves or flat cohomology. These groups have resulted in several publications which an undergraduate has a much better chance of understanding...and in fact there was a (well, extremely bright) undergraduate coauthor on some of them. Even more recently (since December 2013) I have gotten involved in a research program at the border of number theory and combinatorics in which some of the important results are really at ground level. So nowadays if a prospective PhD student finds their way into my orbit, they can probably grab onto something they can understand.
- Have a web presence that is attractive to undergraduates.
To be honest, I feel that I do this rather well. I have an enormous quantity of lecture notes, starting at the advanced undergraduate level. I often get contacted from undergraduates about these notes. Unfortunately though I do not know that anyone has enrolled in our PhD program because of this. The closest I can think of is that a faculty member at a top school told me that he recommended UGA to his students because he thought I would be a good mentor based on my webpage (and indeed we got a couple of students from that school).
This is @ff524's suggestion, and it is a very good one. We have done REUs at UGA, and two of our current PhD students participated in them. If a student has a successful REU experience but does not have the profile to get into a very elite PhD program, it is very natural (and actually sensible) for them to want to continue working with the same faculty or at the same program. In fact it is kind of ideal because you are modelling the experience you want the student to have. Of course not everyone who wants to run an REU can, and if this brings one student per year into your program you are doing extremely well.
- Have a critical mass of happy, successful, sociable female and minority students.
Of course this is a bit of a Catch 22, but it's something to keep an eye on in the cultivation of your current students. If a prospective female student shows up and doesn't see enough other female faces, or if the female faces she sees do not model the kind of experience she wants to have, she is more likely to go elsewhere. Similarly for minorities. Encouraging female students to organize as a group may seem awkward at first but is probably a good idea (and one with a lot of precedent). Having such a group can make them more comfortable and productive, and when a prospective female student comes to town, they will naturally be welcoming.
- Cultivate and exploit regional pipelines.
The thing which is most frustrating to me about graduate recruitment is that so many students aren't considering my program because it is in the Southeastern US and they're only considering programs in their region. (To give an example, we get a fair number of students from Florida. When I ask them why they come to UGA, the most common answer is "Because I'm used to warm weather and it's the farthest north I felt comfortable going." These are people who are going to be happy to get a suitable job anywhere in the US upon graduation.) But sometimes two students from the same region or same institution enroll in your program in the same or consecutive years, and then all of a sudden for a little while people from that place are primed to come. My PhD program admitted two students from the same tiny Central American country in consecutive years. (Both students have since done strong thesis work and graduated.) And then the following year a third student from that country applied. We had an especially strong applicant pool that year and didn't accept him. I happen to know that he went to another, slightly more highly ranked, US PhD program and seems to be doing quite well there. I wish we had kept the lines open.
- Develop relationships with colleagues at liberal arts colleges.
Since you have a PhD program, you are almost certainly not at a liberal arts college, and in fact most good-but-not-elite PhD programs have little natural interaction with good-but-not-elite liberal arts colleges: we run in different circles. This makes it hard when students from such places apply: a student who gets perfect grades while taking only undergraduate courses, has letters saying they're the best student in the last few years from faculty you don't know and who has okay but not great GRE scores is kind of a black box: they could do excellently in your program, disastrously, or anywhere in between. If you can cultivate personal contacts at these places you can get much more information and maybe you can leverage the dynamic the other way: probably the faculty at a top 50 liberal arts college do not have many top 50 research university faculty on speed dial.
- Encourage -- and fund -- dynamic faculty to make recruitment visits.
When I get the chance to visit a new department I usually have a blast, and because I have a shallow knowledge of a lot of different parts of mathematics I have sometimes had the experience of going door to door, talking to each faculty member about their work: not super deeply, but enough to make a positive impression. (And you could send people in my department who would do much better than I would, in particular people who give amazing talks.) However I almost never travel to a place unless I have been invited by someone that I already know, who is willing to fund my visit. I have been to the majority of the top departments (at some point, anyway) but only a small minority of the departments whose undergraduates we could be best recruiting from. If my department had the funds to send multiple faculty members around for multiple recruiting visits, we could make much better connections that would reinforce a lot of the points above. Apparently we don't have funding for this, but maybe we're not trying hard enough.
