I've been running "heavies" in .223s with long barrels in F-TR for many years. The main impediment I have encountered to load development in a brand new barrel is usually brass life, not the barrel "speeding up", which can be accounted for using charge weight. FWIW - I think it would be asking a LOT to expect your new barrel to speed up by 200 fps velocity. Something like 50 fps, maybe as much as 75 fps might be a more reasonable expectation.
As a general rule of thumb, pushing heavies (i.e. 85 to 95 gr bullets) to velocities over 2800 fps with the small .223 Rem cartridge typically means pressures that are close to, or possibly even over the SAAMI max of 545K psi. In my hands, this often causes extremely poor brass life. This problem may be exacerbated by the fact that .223 Rem brass typically grows by at least .005" to .008" at the shoulder during the first firing. Because it is [relatively] short with respect to the chamber, .223 Rem brass is even more susceptible to blown primers when using full-pressure loads in virgin brass. The firing pin pushes the case forward until the shoulder bottoms out in the chamber, leaving a slightly larger gap between the base of the case and bolt face, which allows the primer to come out. I don't really understand exactly why a few thousandths larger gap would create a problem with blown primers, but it does. Once a primer is blown, the case is ruined due to enlargement of the primer pocket. For that reason, I generally fire-form .223 Rem brass using a reduced load that is well below SAAMI max for the first firing. This approach also takes care of the the barrel speeding up process, as that should be complete by the time the fire-forming is finished.
If you choose to use a similar reduced load fire-forming approach, I'd expect you might find a very nice node for the 85.5s somewhere in the 2725 to 2775 fps range. I routinely use such reduced loads with other heavy bullets (88s, 90s, 95s) in practice and/or local club matches, and they can shoot extremely well for that purpose. After determining "optimal" charge weight, I try to cover a reasonable seating depth test range. It is usually pretty obvious where the various .224" heavies want to tune in with respect to seatinmg depth optimum, as in the groups often shrink from perhaps the 0.3 to 0.5 MOA range down to one ragged hole when you find the sweet spot. If necessary, you can start using a .005" increment in order to cover a greater seating depth range, then re-rest some region of interest using a finer increment such as .003".
The key to maintaining such a fire-forming load is to monitor velocity carefully at every outing, because the barrel will speed up as it becomes lapped in by the continued firing. Thus, you may need to decrease the charge weight by a tenth grain or two from time to time to maintain the same velocity you obtained during the load workup earlier in the barrel's life. It's really not that big of a deal, I've done this for years with every new .223 Rem barrel I've used, which is quite a few. At the end of this process, you will have fire-formed brass where the casehead may be slightly work-hardened, but more importantly, where the shoulder will only be bumped back .001" to .002" during the re-sizing process, thereby minimizing the chance for blown primers with subsequent full pressure loads. You will have a fully lapped-in barrel, and you will have developed a better feel for how the rifle/load performs, and what it wants in order to shoot optimally. I view these all as being beneficial for developing a full-pressure load.
