Regarding routes, I yield to others who have hiked a greater diversity of routes in the Pyrenees (especially to Roger who has hiked GR10, GR11 and HRP), but thought I'd chime in about your concerns about access to food. Jim and I walked the HRP abut have not been on any other trails/routes in that range.
On the HRP there are several fairly long sections without a food store (at our pace 5-8 days between stores). However, in those sections there are staffed huts on a pretty regular basis and those huts serve food, even if you're not sleeping there. So if you got grounded by storms and ended up taking longer than expected to travel to the next store, you could camp outside a hut (or get a bunk in the hut) and take meals at the hut so as not to deplete your food supply while waiting out the storm. In our limited experience, the huts served a limited menu all day long. I suspect you've seen it already, but in case you missed it, take a look at the Re-Supply and Restaurants/Refuge sections of our trip report - not that you would eat in the same refuges, but it should give you comfort to see how often we had access to food:
We bought food in the stores assuming that we would not be able to find food at refuges; we didn't adjust our schedule in order to eat evening meals at refuges, but we found that nearly all of them were willing to feed us at whatever time of day we showed up. We passed numerous refuges without stopping to eat.
Also, we don't hitch while hiking, but you would have the opportunity to leave the route to access food stores more frequently if you found your supplies dwindling to an uncomfortable level.
We didn't carry gps device, but given your diabetes, I'd recommend taking a gps device that lets you load good maps so you can carry maps of the surrounding areas in case you need to leave the route unexpectedly in order to get food. If you've got an iPHone then you could carry the IGN maps as well as the OpenCycleMaps and Satellite images; not sure what Garmin provides; Android would give you at least OpenCycleMaps and Satellite images, not sure about IGN maps. Get a gps file of ALL staffed huts, including those off route, giving you info you'd need to leave route to access food. You could do this on paper maps, but the $$cost and weight of carrying paper maps of the lower elevations on the Spanish and French sides in addition to the maps of the route itself would start to add up. I'd carry paper maps of the intended route, with additional map coverage electronically.
The HRP in July/August when we hiked it had plenty of people around; it's not an "alone in the wilderness" experience. In the lower elevations, especially in Basque country, we saw few hikers, but there are nearly daily villages. The higher sections through the middle of the HRP had plenty of hikers. "Going solo, with diabetes, to a foreign country, up into unfamiliar territory can be terrifying." Again, I can't really speak to the added complexity of diabetes, but I wouldn't spend another minute envisioning that you'll be in unfamiliar territory going solo -- there are super-friendly people around (other hikers and staff in the refuges) and if you're a social friendly person you'll be making friends and hiking with others on a regular basis should you choose to do so. Although many of the locals tending shops and refuges don't speak English, nearly all of the hikers we met spoke at least basic English, if not fluent English.
About route finding... if you have good mountain sense, and aren't intimidated by travelling without a well-marked tread, then you'll be good to go. Based on your photos, I wouldn't worry about this. I wouldn't say that to somebody who has only hiked on well defined trails, as you do need to be able to pick a route through rocky slopes in foggy weather, and although there are rock cairns to guide you we frequently found that there were cairns leading in all directions, so we became very wary of cairns. We believe that cairn building is a national past-time in the Pyrenees.
Good luck, and have a fantastic trip. AmyL and Jim
P.S. - we'll be tapping your wealth of knowledge about hiking in Japan sometime in the next couple years. Taking a 5 or 6 week thru hike in Japan is in our top tier, but probably not in the next twelve months. I'll get back to you when we start serious research :)