I am also a retired guy (68) and I rode most of the TransAmerica Trail earlier this year — from home in North Carolina, I rode north to Troutdale, Virginia and followed the Trail from there to Astoria, Oregon. Then I rode on up to Olympia, Washington. Because I needed to be in Washington in early July, I left home quit early in the season. I met very few riders until Lolo Pass on the Montana-Oregon border and those I met were almost all solo riders. On Lolo Pass I encountered the TransAm racers headed east and after them I began meeting east bound touring riders more frequently. Again I met a lot of solo riders and those who were traveling in a group were mostly in groups of two. Four times there were other riders where I camped, twice there were other riders at churches I stayed at, and once there were other riders at a hostel I stayed at. I really enjoyed the evenings with other riders to talk to.
Riding with a group of thirteen and having someone working out the logistics of the trip for you would be a very different experience than going solo. I suspect some people would enjoy both kinds of trips and others would be happier doing one or the other, but not both. A lot of the people I met were surprised that I was riding alone, but, as I say, I met a lot of solo riders; and a couple of them had started out in a group.
I carried a stove and pot and would do that again. I only ate at restaurants about a dozen times. The route is mostly rural in nature and often skirts the edges of the bigger towns. I didn’t have a cell phone on the trip — big mistake, but if I had, I likely would have been able to find more restaurants. Even so, finding restaurants at meal times would be tough. Some days I passed one or no gas stations with food and some of the camping spots would have been long after passing a chance for dinner and long before a chance for breakfast. I have been off caffeine for a few years and that makes travel and camping easier, but if you are addicted, good luck without a stove.
I don’t think I can help with the solo or group decision, but I feel strongly about taking a stove. It is a long trip and having a good dinner and breakfast every day will go a long way toward making the trip more reasonable.