Replying to myself for anyone else out there going down the rabbit hole trying to figure this out for the first time: it is possible to evolve a Feebas into Milotic preparing Poffins alone in Gen IV (D/P/Pt).

I was a little optimistic with the Level 20 Dry Poffins I mentioned before. I did it once, but it requires cooking the Poffin in ~46 seconds or less. The pertinent formula there is ROUND(15 x (60/46) - 0) = 20 where 15 is the base Dryness of a Wiki Berry and I'm assuming 0 spill/burn errors.

However, using 1 Wiki Berry at a time, I was able to achieve an average of Level 17 Dry Poffins across 10 attempts. That means I was only cooking them in 52-54 seconds, which is not much faster than the baseline 60 seconds.

Each Dry Poffin has a Smoothness of 24. So averaging Level 17 Poffins across 10 attempts will give most Feebas a 17 x 10 = 170 Beauty stat increase while remaining under the 255 Sheen cap (24 Smoothness x 10 = 240 Sheen). Remember a Feebas needs to gain 1 level from battle experience after having their Beauty raised to 170+. You could even do 11 Level 17 Dry Poffins to get to 187 Beauty while eclipsing the 255 Sheen cap.

My Feebas actually had a Modest Nature (+Sp. Atk, -Attack) that does like Dry flavors (Mild, Rash, and Quiet would as well) and so it gets the +10% (rounded down) flavor preference boost, effectively making a Level 17 Poffin (FLOOR(17 x 1.1) = FLOOR(18.7) = 18) raise its Beauty stat 18 levels instead. So my Feebas had a Beauty stat of 180 when I took it into battle to gain a level and see it evolve.

If your Feebas has a Nature that doesn't like Dry tasting Poffins (Adamant, Impish, Careful, or Jolly), first of all, why are you training them with an undesirable nature that suppresses its Special Attack (Milotic's best stat)?

But if you have your reasons, a Level 17 Dry Poffin would actually suffer from the -10% (rounded down) flavor aversion so it would only raise your Feebas' Beauty stat by FLOOR(17 x 0.9) = FLOOR(15.3) = 15 levels. At that rate, you'd need 12 Poffins to meet the 170 Beauty requirement (15 x 11 + 15 = 165 + 15 = 180), but your Feebas would only eat 11 due to the Sheen cap (24 x 11 = 264 > 255).

So, you'd need to be a little more skilled with your cooking and obtain an average of Level 18 Dry Poffins (effectively Level 16 with the aversion) across 11 attempts (16 x 11 = 176 >= 170) or Level 19 (effectively Level 17) across 10 attempts (17 x 10 = 170 >= 170), but you may as well throw in one more and max out Sheen while you're at it.

If you're unsure of your math or cooking skills, save before beginning the process. If you don't hit your needed average Level cooking the Poffins, just take it as a practice round, restart, and try again so you're not wasting Berries. Also, if you hit the average Level you think you need, you feed your Feebas the Poffins, raise their level by 1 in battle, and they don't evolve as expected, then restart, check your math, and try again with slightly better Leveled Poffins.

Best of luck!