There are a couple of ways to address this, and most have them have already been covered.
Vehicular repeater
Have a tech go through the system
Higher gain antenna
better coax,
Tower top preamp,
Etc.
One common way of addressing these sorts of coverage issues is to install a voted repeater system. This would involve installing a receiver out at a location that did a better job receiving than the main site.
To do this, you'd need the receiver, antenna, feed line, antenna support, power and a way to get the signal back to the main site. The antenna can be specifically chosen to cover or not cover specific areas.
At the main site, you'd need a signal comparator/voter to route the best audio to the repeater. The voter would have an input from the receive side of the main site, and an input from the receive only site.
Since receivers don't need to be licensed, as a second repeater or a mobile repeater would, this can save some money.
Where it gets expensive is the backhaul to the main site. Getting clean audio from the RX site back to the main site needs one of the following:
Conditioned circuit from the phone company
radio link
IP link (has to be reliable! No Jim Bob's interwebs services run out of some guys basement)
microwave link.
It might be worth checking with other agencies in your area, they may already have a suitable site with the tower, electric service, and if you are lucky, some sort of existing backhaul you can hop on.
These systems are not the type of thing that the "guy who knows something about radios" set's up. Actually, any of these solutions is going to require a knowledgeable person that can design the system, install it and get it working correctly. It won't be a cheap solution, but it will be cheaper than a second repeater. The nice thing about it is that it's always there and always on. You don't need to have a specific vehicle on site with a vehicular extender on board.
Digital won't work miracles, so don't rely on that as a solution. Anyway, as a fire service, you'd want to retain some analog stuff. Digital doesn't always work well in high noise environments.