It’s really pretty amazing how the beer scene in the US has changed so much that barrel-aged beers have generated great interest and tremendous success among brewers playing with barrels. Barrels do present many challenges not encountered with the brewing of other types of beer. And carbonation after barrel aging is one of those challenges.
I am not going to pretend to know all of the reasons that barrel-aged beers are often difficult to carbonate using normal methods, even when fresh yeast is used. But the two real big issues about these beers are mentioned in your question, and those are high alcohol and very low yeast viability, and cell density following prolonged aging in multiple vessels. I have read that some yeast strains are more or less active in the presence of oak tannins, especially with new barrels. Not sure about how bourbon barrels factor into this calculus. Here are a few ideas of how to carbonate high-alcohol beers with very little to no viable yeast that is in the proper health to contribute much to the effort of carbonation.
The first is to deliver a dose of yeast that is in the proper condition to do the job required. I am fond of kräusening because actively fermenting yeast are in the proper biological condition to convert carbohydrates into carbon dioxide quickly and efficiently. This is different from adding dormant yeast (for example, dried yeast) and sugar to a bottle of beer. Dormant yeast have to “wake up,” prepare for metabolic activity, transport carbohydrates across their cell walls and crank up the metabolic machine before any carbon dioxide is produced. This is referred to as the lag phase of cell growth and occurs before microbiological cultures begin growing. The bottom line is that adding yeast that are awake and making noise gives you a better shot at carbonating these beasty brews than adding inactive yeast.
The type of yeast can also be a real factor with higher alcohol beers. Years ago I questioned the alcoholic strength claimed by many brewers and chalked some of the high claims to a blend of bravado and faulty math. Not so today as the art and science of high alcohol beer brewing has become better understood. Add to this the alcohol contributed by wet bourbon barrels, for example, and brews topping the scales at 13.5% ABV are not such an oddity. The alcoholic strength of your beer is surely a problem for many yeast strains. The use of a more alcohol-tolerant yeast, like Champagne yeast, is definitely worth considering for these beers high in ABV. Be careful, though. Your beer may have some residual fermentables if the fermenting strain was not able to deal with the high alcohol. Adding a different strain at bottling time could present an issue with excess carbonation and bottle bombs if your beer has a lot of residual fermentables. This may not be an issue, but is something to keep in mind. You could do a small test fermentation if you have serious concerns.
I have saved the easiest, and least sexy suggestion, for last. Rack your beer into a keg, add carbon dioxide head pressure to add the level of carbonation you seek, and use a counter pressure bottle filler to fill your precious beer into bottles for safe keeping. The real advantage of this method is that the level of carbonation can be checked prior to bottling and the potential for over-carbonation or under-carbonation due to bottle fermentation issues is about nil. What I like about this method is that the beer flavor profile is more-or-less set when you bottle, and that the flavor changes that occur during aging have little, if anything, to do with changes in carbonation. Hopefully this information is useful to your endeavor!