Transmission dilemma

Chris; I think you might be in a bit of a pickle
The Wallace Calculator says; if your
Static compression ratio really is 8:1, and
Ica of 64*(268/276/114 cam); and 640 ft elevation
Effective stroke is 2.57 inches.
Your dynamic compression ratio is ............ 6.43:1 .
Your dynamic cranking pressure is ............ 119 PSI.
V/P (Volume to Pressure Index) is ............... 94VP
read about VP here; V/P Index Calculation
At VP of 94 your 340 is gonna come off idle, feeling just about like a 273.(see below)

With 3.07 gears it will be even worse, and the unknown stall speed is probably gonna hurt real bad.
The only thing you got going for you with this combo, is the cubes and the lighter weight body style.
As a cruiser this might work, but I don't think there will be much fun in it until you get the Rs up; Ima thinking she will begin waking up around 3500rpm/33 mph, in first gear, and start pulling at 4000/38 mph.
If you're OK with that, then have at her, but you'll
probably want to paint it red,and tell your friends it's a 273.
Because;
Here is what a 273 looks like in terms of low rpm performance;
Static compression ratio of 8:1.
Ica of 48*, 640 elevation
Effective stroke is 2.89 inches.
Your dynamic compression ratio is ................ 7.10:1 .
Your dynamic cranking pressure is ................ 136PSI.
V/P (Volume to Pressure Index) is .................. 98VP
Notice the VP is higher than your 340 is, and the 273 with it's tiny cam, is making more pressure than the 340. An additional penalty with the 340cam, is lousy fuel-economy.
But the good news is a new smaller cam can be slid in at any time into a low-compression engine, with nothing but good results.

Here is a 360 2bbl type cam, with no other changes
Static compression ratio of 8:1.
Ica of 54*, still 640 elevation
Effective stroke is 2.78 inches.
Your dynamic compression ratio is 6.87:1 .
Your dynamic cranking pressure is ................... 130PSI.
V/P (Volume to Pressure Index) is..................... 112VP

112VP is still nothing special ; in comparison, a 5.2 Magnum makes over 124VP. But it is an improvement of; 112/94= plus 19%, which is about the same percentage as going from 3.07s to 3.66s, in terms of bottom end performance improvement.
I know you're on a budget, but since you do not yet have a rear end, there is no way I would suffer this combo with 3.07s. I would leave the 7.25 in the back with whatever gears are in it (but with an oil change); your 340 at this point cannot hurt it unless you start peg-legging it. Don't do that! And I would take that money you saved and get yourself a higher stall TC; at the very, very least a 2600.
If that 7.25 is a 2.76, your combo will still be real soft off the line, but at least you can cruise 70=2570 at zero-slip.

Here is my reasoning;
Lets say your 94VP bring 240 ftlbs to the crank at 1800/2000 stall. By the time that gets to the rear axles, And at zero mph, it might be an instantaneous;
240x1.6TC x2.45x3.07=2890 ftlbs@zero mph out the back, and 70=2890@zero-slip.
whereas;
at 2600, I'll guess the 340 brings 280ftlbs to bear, then with 2.76s
280x1.7TC x2.45x2.76= 3220ftlbs@zero mph out the back, and 70=2600@ zero-slip.
Notice the instantaneous ftlbs has risen from 2890 to 3220, WITH a cruise reduction of 290.
So if my guesses of 240 and 280, or even just the ratio of 240 to 280=1.166, is anywhere close, then you can see that the 2600 is gonna be a big improvement;
3220/2890= plus 10.7% in take off, and
2890 less 2600, is a 290 rpm improvement in cruise rpm.
These are big deals.

But if your current 7.25 happens to be a 3.23, well; there is no saving the cruise rpm cuz 70=3040@zero slip. Your best solutions are taller than 25" tires and slowing down. All my calcs thus far have been with 25" tires.
In this case,(with 3.23s) you can keep your current TC which I'm guessing is gonna be between 1800 and 2100tops, and your new take-off could be
240x1.6TC x2.45x3.23=3040@zero mph; that's bearable with a 340, now you can at least spin the tires for a lil ways (get a SureGrip asap); and now, you can
paint your 340 turquoise.
With the money you saved by not buying a Jeep rear, nor a hi-stall, treat your car to an A999. and hope for 2.76s in the 7.25. Thus;
240x1.6TC x2.74x2.76=2900ftlbs@zero mph, and 70=2600. Compare this to the first math I did above, in blue.
240x1.6TC x2.45x3.07=2890 ftlbs@zero mph out the back, and 70=2890
Notice the take-off is about the same, but the cruise Rpm is down to 2600 from 2890, being 290rpm.
And you don't have to beat the snot out of your tunnel. The A999 bolts right in. Physically, the A999 is practically identical to the A904, just with all the best Mopar guts in it, the new ratios of 2.74-1.54-1.00, and the loc-up TC which is good for between 220 and 280 cruising rpm reduction. And the TC stall is usually slightly higher than a 904. The early models had a hydraulic loc-up, controlled by the VB,automatically.
The only thing you have to remember is the engine balance, which has to be transferred to the new flexplate. Rebuilding these A999s is easy-peasy.

I hope you realize that these changes are a direct result and correction for the very low cylinder pressure in your 8/1 Scr 340. If she was the earlier model 340, you could just slam anything together.

By the way, about 1975, I slammed a 340 short block together with a 318 cam and top end; heads and 2bbl. Hey, its what I had and I was ~21 years old. I dropped that into a 65 V100 wagon, I think you Americans called that a Dart. I had to get fenderwell headers to make it work, which was my major cost. This was my all-time favorite swap. I used an A904 from a 273, and the wagon's oem 7.25 with 3.23s. The trans went out first, with me driving the crap out of it. I think I got three summers out of it.
That 340 tho, was the hi-compression model. I still have it, but in boxes now,lol. I still got the trans too,lol. In any case
just trying to help.