There's absolutely no point in going into a situation like yours without performing a COMPLETE rebuild. There's just too much stuff that needs to be done to build a transmission that's going to live. First of all, ask them what they plan to do for your $$$. They are working for you! If any shop says that they're going to just replace the 3-4 clutch, turn and run...especially for those prices! I could, literally, replace your 3-4 clutch stack in about 15 minutes, but doing that would be pure lunacy!
As a 'for instance', in my shop, I would build you a 'Stage II' package, as I do for most F-bodies. The basic build is generally the same, but the specifics are always done on a case-by-case basis, depending what you, my customer, are looking for in a finished product.
My 'Stage II' package come in at around $1000 (bench build), without a converter. When I build ANY transmission, there are literally no two parts still assembled when it goes through the parts washer. EVERYTHING comes apart and is inspected - especially in a 4L60E! Every piece of the pump, every valve in the valve body, EVERYTHING!
I buy most of my parts in bulk, so a 'kit' does not really apply to my parts list, but a partial list would look like this:
Borg Warner frictions (7 disc high energy in the 3-4)
New OEM AC Delco 3-4 apply plate and backing plate
Kolene steels in forward and 3-4 clutches
Turbulator steels in reverse input and low/reverse
Bonded steel 3-4 clutch piston
Borg Warner low roller clutch
Borg Warner dual cage 29 element forward sprag
"Beast" sun shell
Wide forward and rear stator support and reaction sun gear bushings
Teflon pump bushing, babbit case bushing and most of the other bushings
Complete paper and rubber kit (obviously)
New shift solenoids, pressure switch manifold and 3-2 downshift solenoid
.500" boost valve
Yada, yada....
If you want a complete list, I can get you one, but my point is that there is absolutely no point in doing any kind of partial build on an automatic transmission. Also, notice that nowhere in my list did you see a Transgo "shift kit". Do yourself a favor and don't let anyone put any of that DIY-grade junk in your transmission. If the shop doesn't know how to modify your shift characteristics without a "kit", then walk away...