any benefit to swapping heads?

Well that kindof depends on what your current set-up can do at low rpm; but yeah if you don't want to bring the compression up, then I would pull that cam in a hearbeat. I would not be able to stand that low a VP. And swapping out the cam is the quickest,cheapest,easiest fix.

The differences in the first gears of all the A833s by themselves,are not enough bring this combo up to a satisfactory performance level. Your VP is just too low.
The odds that you have a 2.47 low are pretty slim.
The odds that you have a 3.09 Commando are even slimmer.
Leaving you with a 2.66 standard box.
But let's say you did currently have a 2.47, and you went to a 3.09; the advantage would be 25% in the first gear alone.
Then as your VP might be close to 82 as estimated in post #55, totally estimated best guess. Say your 340 was able to put out 150ftlbs at 1800rpm. With a 2.47 low and 3.55s this would be multiplied to 1315ftlbs not enough to break those 275/60s loose, am I right? Ok so the simple solution is to just rev it up until you find enough power. Yeah that works but ..... it ain't impressive. And it doesnt solve driving at low-rpm.
But with a 3.09, this maths out to 1645 ftlbs. So maybe your 340 will bust 'em loose,maybe; but I see more of a chirp and a bog, until you get the hang of it. It certainly will not be impressive. Again just rev it up til you find the power, which will now be at quite a bit lower rpm. And it still does nothing for driving at lower rpm in any gear.Which with a manual trans, happens a lot.
Now the cost factor to get that 25% is ridiculous. I mean that is a complete gear swap.
But the rear gear option is just as bad; it would take the same plus 25% gearing or 4.44 gears to equal that improvement.
To my way of thinking this combo really really really needs cylinder pressure, or a much smaller cam. Did I work that out in post #55? lemmee check. Nope I don't see it,
so here is your 8.2 340 with a 252/112 cam in at 108;still at 800ft. This is a stock 360 2bbl type cam. There are other better 252 type cams.

Static compression ratio of 8.2:1.
Effective stroke is 2.78 inches.
Your dynamic compression ratio is 7.04:1 .
Your dynamic cranking pressure is 134.04 PSI.
V/P (Volume to Pressure Index) is 115 .

Look at that VP jump! This is very significant 40% better than the 82VP originally estimated. Remember this is a measurement of performance that is only relevant up to in the range of 3000 to 3500 rpm. So consequently this 252 cam may make less power from about that point on; it will not have a top-end rush. That doesn't mean it will stop reving; mine in a 318 went to 5500 regularly and to 6000 occasionally with appropriate springing. It just means it runs outta power about 800 to 1000rpm sooner than your 284.
But I tell you what, I bet that 252 cam will hit 5000rpm/44 mph, sooner than your current combo,lol.
Oh yeah, 115VP should be enough to smoke 275/60 BFG radial T/As with 3.55s, hyup, once you get them rotating. So for $200 bucks or so in parts, this is a cheap fix.

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And if you do want to be impressive with that 252 cam, swapping to the 3.09 Commando box and say 3.73s, well, Shazzam! you're all set up for 60mph@5150 at the top of second gear; let 'er rip! And this cam might make 25 ftlbs more at 1800 than your current combo, so lets call it 175@1800. (it might even make 200,IDK).And that would get you 175 x 3.09x3.73=2017 ftlbs; more than enough to break the 275s loose and impressively. Now you can put on the line-loc and bring the Rs down closer to an idle, and make the tires moan,howl,wail, or scream..... and that's impressive. Well, it is to me when I do it,lol.
But say you kept the 2.66 box and went to 3.91s. Now your starter gear is 10.40 and times 175@1800=1820ftlbs and still just enough to spin, and now you have the VP to sustain it with the 252 cam. This is also a cost-effective swap...... except of course the hiway rpm jumps to 3050. And the 252 is well able to pull 2.45s to do 65= 1911.
If you are willing to learn to adjust your valves about once a year, you could switch to a solid lifter cam and pick up few horsepower, without a loss in VP, but IMO, with log manifolds, and at this cam-size, it's hardly worth it.

Ok it just hit me.
that 252 combo is just begging for the 3.09overdrive box and 4.10s. The starter would be 12.67 and times 175 would be 2217 ftlbs @1800 for massively impressive tirespin,lol. Your hiway rpm would be 65=2334, and 60 would be a tic under 5000 at the top of second....... so we could advance that cam just a tad, say to an ICA of 48*
Static compression ratio of 8.2:1.
Effective stroke is 2.89 inches.
Your dynamic compression ratio is 7.28:1 .
Your dynamic cranking pressure is 140.29 PSI.
V/P (Volume to Pressure Index) is 125 .
There you go; 140psi/125VP; that's a pretty good number, and that will pull the splits in that od-box reasonably well with 4.10s lol. I would even try it with 3.91s. and the best news is up here I have bought those od boxes for as little as $50C at swap meets.
This is not an ideal situation to be sure, but for the cost of a cam-kit, a swap-meet od box, and a set of gears installed, IMO you will end up with a pretty exciting streeter.
Here is a gear ratio comparison. First
9.44-6.82-4.97-3.55 ..... your most likely current set-up, and then
12.08-6.53-3.91-2.85 ......the od box/3.91s
Notice second gear is practically identical.
Notice the wicked starter gear, that will help your 252 cam roast tires.
Notice the hiway gear, that will get you 65=2226rpm
Notice the crappy third gear that you will almost never use, as a streeter, at WOT, so who cares how crappy it is.
Second gear is the most important gear. You will spend more time in second than in any other gear, not including hiway time.This 6.53 ratio has to pull from 1500/18mph to 3600/40mph. This is it's home, and the 252 cam will pull well in that range,very well. And that same gear will pull all the way to 65=5100..... just about right for that cam,nay,just about perfect.
Well, with that starter gear, I might put the cam back to a 50*ICA, and pick up a little power in that Looooooog pull to 65,lol.
Ok I gotta work tomorrow so TTYL