Len Backus is pretty close to on track in his comments in my opinion.
Lilja's tests were with very large high volume cases in the .308" or .338" calibers.
In your case, you are dealing with a relatively low pressure round at least in factory loaded form.
More importantly, the 375 H&H has a relatively small case capacity to bore volume ratio so you are able to use faster powders in the larger bores with much less worry of pressures.
This is because as the bullet travels down the bore, the ever changing chamber volume, the entire volume behind teh bullet, increases very quickly so that the faster powders have plenty of room to expand rapidly.
This is why these style of rounds are so efficent in shorter barreled rifles.
It is also the reason that they do not gain a great deal with longer barrels and also why they do not make a muzzle brake
By the time the bullet reaches the bore, the pressure in the bore has dropped considerably so teh acceleration of the bullet is relatively low at this point at the end of the barrel.
Especially compared to a round like the 375 RUM or 378 Wby.
75 to 80 grains of powder simply runs out of expansion in this size of a bore to continue to add significant velocity in barrels from 24 to 28".
YOu will probably be looking at a true gain of more like 15 fps for the 375 H&H going from 24 to 28".
In my mind, if you are going with a 28" pipe, cut the barrel to the 375 RUM chamber, especially if you want that 200 fps gain over the 375 H&H.
Otherwise you will be reducing the fine handling characteristics of the 24" H&H rifle with no real improvement in performance.
The RUM with its +100 gr capacity will run much faster in the 28" barrel as will the 378 Wby but the RUM recoils quite smartly and the 378 can be rediculous as far as recoil goes.
As a rule of thumb, rounds with large bore(375 and up) to case capacity ratios will gain 10-14 fps per inch of barrel past 22".
Medium bores(30-338) with medium ase volume such as the 300 Win and 338 Win will average in the 15-18 fps range with barrels over 24".
Small bores(6mm-7mm) with medium case capacity rounds such as the 243 Win to 7mm Rem Mag will gain about the same 15-18 fps per inch over 22".
Medium bores(30-338) with large case volumes such as the RUM cases will gain 18-20 fps per inch over 24".
These bores with huge case volumes like the big Wby case and similiar cases will average around 20-23 fps per inch over 26".
The idea that you will get 50 to 65 fps for each inch of barrel is kind of a myth in our sport. If you had to average all the rounds I would say your looking at around 18 fps per inch of added barrel length over 24".