We can't tell if the lack of teaching experience will hurt you or not; too many variables. But I can share with you how to prepare yourself on this front.
Make a clear inventory of all your guest lectures, reflect on them
Do know that most job market candidates have not taught a full course themselves and nearly none of them had developed a course for real by themselves. Your profile is definitely not in the dismal category so you shouldn't beat yourself up too much. In the teaching experience section, list all of the relevant guest lectures you have done, and make sure to highlight the 2-month one, as it's already 2/3 of a semester. If you can survive 8 weeks, you can likely survive 13 weeks.
Do also recall the title of your talk, class size, undergrad or graduate students, any in-class activities you have used, any evaluations you have applied (assignment, quiz), and if you can get a hold on your colleagues whom you helped, check if their course evaluations had any entries that are pertinent to your performance and ask if they would allow you to quote them.
Also, since it's a research institute, it'd be important to document your 1-on-1 mentoring experience as well. Any entries on supervising students or postdocs should also be captured.
With this inventory listed in front of you, try to dive deeper to remember how and why you explained the concept a certain way, why you decided the sequence of slides/notes were better this way. New teachers often worked on hunches, but most hunches have some reasons behind them. And most of them are a direct manifestation from their experience as a student. So, in fact I think it's totally fine that you based some of your teaching philosophy on your student identity.
Develop a clear set of vocabularies in learning and education
There are a few titles I enjoyed and found useful when learning how to teach:
If you have access to these titles, definitely check them out. You should be able to garner a healthy amount of concepts and vocabularies about teaching, and apply them appropriately in your teaching statement. By the end you should be able to sensibly talk about things like Bloom's taxonomy, backward engineering of syllabi, action words in learning objectives, summative and formative assessments, etc.
Some schools (perhaps your current one as well) periodically conduct teacher development workshops. While you're there you can also try to enroll in some of them, or at least contact them for online or published references on learning theories and teaching methodology. They will also be an excellent source for sample teaching philosophy.
(I think) there is no recipe for teaching philosophy
I have come to a conclusion myself that there really isn't a golden formula for how to write a good teaching philosophy. It is really an authentic statement about your current teacher's state of mind. (I looked at my teaching philosophy written 4 years ago and I found that silly as well.) A little bit of naivete is not going to hurt you.
What I found, however, is that it's easier to develop this document if you sit down and ponder about 3-5 statements starting with: "I believe learning should be..." and then elaborate from there. If you have done your inventory and literature review meticulously, you should be able to come up with a few that resonate with you.
It is also common to mention what kind of courses you're ready to teach. Most committee members would find that easier to imagine how to incorporate you into the teaching roster.
Seek help from peers
And since you mentioned you have helped some other faculty pals, definitely consider getting their feedback on your teaching philosophy. The people working at the faculty development will also be a good resource if you don't wish to publicize your job hunting.