Back when the .243 came out there was quite a flap... .243 WCF had a 1 in 10 twist while the .244 Remington has a 1 in 12. The .243 would shoot 100 grain bullets, pointed bullets o.k. which is what the deer hunter wanted. The .244 would not shoot the 100 grain pointed bullets satisfactorily and even with "massage" (i.e. the re name to 6mm Remington with a 1 in 9 twist) hasn't equalled the .243 popularity with its regular 1 in 10 twist... .244 would shoot 100 grain round noses fine. Oh wellll... Some argue that the 6mm Remington is a better "alll around" cartridge... longer neck is often mentioned... Your money, your call. Making .243 cases from .308 keeps it popular... (with cheap skates)
You speak of a custom rifle. Fine. Most commercial bullet brands in USA stop at 100 grains and there are some "game bullets" that are 90 grains. 1 in 10 is fine for these, points and all. The competition crowd have to try heavier bullets, key word here it "try." ... And they build rifles around there latest guesses. 1 in 9 is good too. No it will not hurt you much with lighter bullets. If the bullet is "unbalanced", less quality, the faster twist will make this show up faster. If the bullet is good... And there is a discussion of the killing power of a bullet spinniing faster. Forward motion is lost rapidly to air resistance. Rotational motion is not lost nearly so fast. So if you wish to go 1 in 8 or faster... The Swedes have been quite happy with their 6.5 Swede Mauser which I believe is 1 in 7.5 or so in inches. benchrest.com has lengthy articles by top flight barrel makers. You might care to consider what they have to say.
Swage.com has a list of bullet makers that will make you whatever you are willing to pay for. You might want to try "semi pointed" for more weight and and acceptable length. There is a 70 grain .224 used in US on deer, very semi pointed. Winchester has a 64 grain too, more pointed. Otherwise, rebarreling your .22/250 to .243 should not be a great problem... It is a balancing act and you need to be happy. luck.