Is the assumption that LENR "excess heat" is only generated by the thermalization of gammas?
No, obviously there are other high energy particles, and not all reactions generate gammas.
But, if gammas are generated (as is the hypothesis for the RG experiment) then they will normally contain significant amounts of the released energy. I build into the above a factor of 100 - e.g. 1% of released energy going into the gammas. In fact if gammas are generated they are likely not to be thermalised within a lightweight calorimetric enclosure, so this is in addition to the thermal output. To get very low ratios of gamma energy to other (thermalised) energy you need branching ratios that just happen mostly to give reaction products thermalised, and only very occasionally gammas. That is possible, but not likely. You can always make any data fit a hypothesis as vague as LENR by choosing unlikely options, and maybe they happen, but I'm skeptical when they do.