And that part seems entirely reasonable. It looks like the Tomahawk cruise missile did it with an 84 lb package with a 16-bit computer with 64K of memory [1] [2] and sensors. That's similar computing performance to an original IBM PC, which weighed 30 lb. The only bit of hardware an iPhone doesn't seem to have for TERCOM is a radar altimeter, but it looks like those are available for civil aviation.
[1] https://www.forecastinternational.com/archive/disp_pdf.cfm?D... ("AGM-109/BGM-109 Tomahawk ... Litton 4516-C digital computer with 64K memory")
[2] https://www.forecastinternational.com/archive/disp_old_pdf.c... ("16-bit LC-4516C digital computer")
Ardupilot boards are $20 and support lots of different altimeters technologies: https://ardupilot.org/copter/docs/common-rangefinder-landing...