Yep, you're on the right track with shortening the lead, but if it means causing damage to the chimney don't do it. I would suggest that since you're only looking at driving 3 devices (2 x TV and FM) you leave the mount as is and just go with a single in/single out 10db amp (you can get a reasonably priced RCA 10db amp at Home Depot or there are much higher quality ones out there). You should put it inside near where the cable enters the building, but bear in mind you'll need to supply 120VAC to power it wherever you mount it. You don't want to have the amp any closer to the antenna because amps are noisier than preamps and you want the signal to be as clean as possible for as long a distance as possible. If all the amp has to do is drive the internal cabling it will do just great. Amps don't need to be so stringent about noise as preamps because internal cable runs are comparatively short and shielded.
You asked about a high output amp (15-20db) but that level of signal could damage some gear, so people who drive their indoor connections with that kind of power need to put 3 to 6db attenuators on all their gear. It may sound redundant, but the payoff is that you rarely if ever have line loss anywhere indoors by adding 2 or 3 more devices.