Are there digital front ends with the body...

Other's will disagree but for me it's my Esoteric DV-50. Yes, my not too pricy TT's do give it run for it's money. The trade off is software. New vinyl is pricy and the quality is not very good. Used vinyl is a crap shoot. Digital software is for the most part cheap and all over the place. Dammed if you do dammed if you don't.

In the two areas you mention, analog (tape as well) kills any redbook CD.
On the other hand, CD can avoid speed variation, bass noise, mistracking,
surface noise, and so on. As computer chips increase in capability, CD's can sound better and better while analog cannot. Some convert analog to digital for processing. The future of analog is digital.

To my ears, the biggest problem for CDPs (as opposed to vinyl) is not the "body" (or lack of) but the dynamics - both micro and macro.

As several have mentioned you need to stick with something specifically designed to reproduce the old analog sound, such as Tvad suggests. Analog has advantages in many areas such as "soft clipping" on tape etc. Many older generation audio professionals prefer analog for certain applications because of how it modifies the sound in a desirable way - for example analog is very good at compression (reducing dynamics) with less risk of sounding bad. Many people prefer that old analog tape sound as opposed to the unforgiving digital sound.

I think it is hard to deliberately replicate this sound using a device that takes CD digital and modifies it (after all, the analog sound is part of an entire studio and manufacturing process).

Doug Sax (of Sheffield labs fame) still uses his brother's designed tube amp circuitry to help create CD masters that have some compression, warmer vocals and a bass kick drum punch. If you buy Doug Sax Mastered CD's then you may find them a just bit closer to old analog sound than others...just two cents.