Also being fairly intimately acquainted with the insides of a Reverb, I reckon it shouldn’t be a problem to fix it with a full service. It’s either going to be the IFP or the plunger itself, and the inner seal head. Maybe a bit of all three, but it’s really just o-rings and maybe a glide-ring or two.
Those 4 videos take up a massive amount of time explaining how not to be an idiot before actually getting into what is a pretty basic piece of equipment. I’ve done a full service with none of the specific tools (step by step instruction on mtbr, but it’s pretty self-explanatory if you think how a Reverb actually works) and it’s fine.