Well it won't be exactly the same since they are the same weight if I'm not mistaken. That means that cutting the longbody back would probably mean a lower swingweight than the regular length frame has to start with.
Obviously the swingweight of the Longbody will drop but, because it's 345 to begin with, removing just an extra 0.5 inch won't make it drop below 327 (swingweight of the regular length Speedport Black) ?
On this particular frame, it's not obvious at all. Looking at the unstrung specs on Prince's site, the longbody is 10 more swingweight units, and balance is the same. Since we don't know how they changed the weight distribution to maintain the balance point we can't say for sure what would happen. I have a guess, but in any case, I think it will take a bit of customization to match a long body to the regular version, and I doubt they would play the same afterwards. Might be pretty close, but not the same.
Yes, it is obvious because on any frame when you remove weight you reduce the swingweight. That is even more so when you reduce the length of a racquet. The amount to swing has become less so the weight to swing will become lower. The only question is how much it will change. My mate cut back a TT Warrior OS and the static weight only changed by 5 grams. I would expect this would be similar.
As to the weight distribution, TW has them listed as being the same weight and balance but the USRSA has the Speedport Black (with ports) at 32.8cm (roughly 5pts HL) , 321grams and 328 swingweight while the Longbody (with ports) is 33.5cm (roughly 2pts HL), 317grams and 335 swingweight.
So, if you removed 1/2 an inch from the Longbody you'd drop the swingweight, make it more head light (probably back to 5pts HL) but you'd also have to add weight to bring it back up to the standard length version.
The strange thing is the stiffness. Although the dimensions of the head are exactly the same the Longbody is more flexible. I wonder if that would change when you cut it back (in the same way that a strung racquet can give a different flex reading to an unstrung one).
All up, if weight and swingweight were the only difference (although they would probably be close) but flex remained the same you could just add some lead tape. It should be close enough to not be a major concern.
Like you said, it's hard to predict, but I would guess removing 1/2" from the SB Long will knock ~20 swingweight units off of it. So if it started at ~335, you'd end up with ~315. If that's too insipid, simply add lead at twelve to bump up the swingweight. ~2.5 grams at 12 would bring it to 325.
I think the flex in this case is purely a function of length - a longer bar of the same inherent stiffness will bend more easily than a shorter one. So I would bet the stiffness of the cut version would be pretty close to the standard version.
I believe they will be fairly close judging from the specs of the Std vs the LB. I would hesitate to guess that they'll be as close two different standard versions, given the poor qc of some the racquet companies.
I'd try it first as a LB, if you don't like it, choke up on the handle to gain a feel of what it might be like as a standard length. If that feels good, first cut a 1/4 inch and if that feels like you're heading in the right direction, cut off another 1/4 inch. I have done this with a Prince Michael Chang LB, Tour 8 V-engine, RDX300, V-Con 17, PST + and a N6.1x, all with no problems.
Yes, it is obvious because on any frame when you remove weight you reduce the swingweight. That is even more so when you reduce the length of a racquet. The amount to swing has become less so the weight to swing will become lower.