woah, great results so far waffle!
Rapidly, I will try and answer some of your questions from our own experience, but not sure there's a right nor wrong way, as a little gut feel is also required (and a leap of faith maybe)?
DD learns piano as 2nd instrument, since age 7. At home, 30 mins a week during term time, now G7 level. Takes 35 mins each singing and violin lessons at school, plus a supplementary 1 hour violin at home. All different teachers, different CVs.
Piano teacher is young, but experienced with main school peri work and private, very busy. It's a bun fight negotiation each Sept to get a slot that works for both. Already too much in-school schedule juggling to fit another lesson there - they do have to catch up on lessons missed at secondary.
I have known many local parents (who are not musical at home) go into our RAM and place their requirements on the notice boards. The students supplement their living this way. I would absolutely do this, if we hadn't got lucky, but continuity is not guaranteed, and maybe for younger learners they need to know they can develop a relationship with their teacher. I used it once for DD's auditions for 11+ and needed an accompanist to practice her pieces with her...it worked a treat.
I'd therefore have no issue in trying in the absence of getting a good, longer term teacher (with availability to come to my home,) as instilling a love of playing as well as developing basic technique would be a key consideration. Piano-playing parents often start this way.
Bit of a fluffy response, but if the talent's on your doorstep, albeit not officially teacher qualified, why not give it a try. Value is a tricky one to measure, but you could just find a gem...