Yes, there is an alternative ...
You might find that a 5/16 NC tap will thread into the inner cap with a grip sufficient to allow you to pull the cap out. That way doesn't require you to drill through the top of the inner cap.
If you are mechanically minded, you might try fitting a drill stop collar to the tap, and using a couple of large washers, create a system where you can pry between the washers to force the tap to pull the cap out. I've adapted a threaded hollow tube used in lamps to the task, and with a couple of threaded metal strips used in electrical boxes have fashioned a rudimentary puller from that.
You may discover other ways - for example, screwing the tap into the inner cap, sliding a couple of washers over the tap, and mounting in a vice. Gentle prying with a screwdriver between the washers should force the inner cap out, without putting too much strain on the lip of the FP cap.
Of course, if light thread marks on the inside of the inner cap bother you, this method may not appeal.
Gerry
PS: Sorry, I forgot to answer your questions. The inner cap is just a friction fit, no threads or glue to worry about, although there is sometimes a fair amount of friction...