I 've shot both tapered and parallel shafts for years. When properly tuned to the bow, they both fly very nicely and most couldn't tell any difference between them. Theoretically, tapered shafts recover faster and perhaps vibrate a little less on impact, resulting in slightly better penetration, but again, I think the difference is so small as to be negligible.
Tapering doesn't reduce the spine very much, from not at all to about 3# plus or minus on most shafts.
When my current supply of tapered shafts is used up, I'll go back to parallel shafts for the additional physical weight they provide. Tapering removes about 30 grains, plus or minus from a 11/32 shaft.
Keep in mind, too, that almost all carbon and aluminum shafts are not tapered. They seem to work pretty well.
You can soften the dynamic spine of a heavy shaft by using heavier points and/or leaving the shaft longer.
If you have an arrow flite problem, it may not be related to spine. With cedars, I've found that I can overspine by 10# with standard weight heads, say 125-140 grains or so, and by 20# with heavier heads, say in the 160-175grain area, with my longbows, and most of them are not centershot. With centershot recurves, you should be able to overspine by almost any amount. Good luck.