Who is still making CD transports?

Here’s a list of CD transports made, from the first to the latest (at time of article). You’ll need to do a search as to which one you want and proceed from there.
https://www.hifi-advice.com/blog/classics/digital-classics/the-almost-complete-philips-cdm-range-of-swing-arm-cd-mechanisms/

The links towards the end of the article are worth a look as well.

All the best,
Nonoise

CEC
http://www.cec-web.co.jp/products/cdplayer/index_e.html

Hello,
Every CD player can be used as a transport as long as it has a digital outs. PS Audio has a great transport. Not sure about the reclocking unless you use the right DAC and type of connection. Ask
Ps Audio first. I feel this comes down to budget. The Cambridge is really good especially if you do some basic upgrades like dampening the cabinet with dynamat. If you can afford a better unit they can sound a lot better. All of the brands mentioned here are really good. Decide what you want to pay. A lot of people at audiogon feel the DAC is more important. I have to agree since there are only a dozen transport companies. If this is just CDs or Redbook then you have a lot of choices. If you need SACDs your choices are limited. Most SACD transports will not play out of a digital out unless you are using the right DAC with the correct hand shake due to Sony. 

Chord Electronics Blu MKII.  Excellent unit that also does upscaling.
https://chordelectronics.co.uk/product/blu-mk-2/

Who is still making CD transports?

The rumor mill is strong and has Schiit bringing one out, and if Mike Moffat (from Theta fame) has anything to do with it, it should be a cracker, at budget biscuit pricing.
Flick them an email, see if you can get anything out of them.  info@schiit.com

Cheers George