Curious question posed here!
I don’t have any experience with the setup you describe however I do own a NAIT XS (-2 fascia upgrade version) and used to use that with a HiCap DR.
The setup I currently have includes a CD5 XS which has the benefit of a BNC S/PDIF output which I connect using a Naim DC-1 digital IC to a ND5 XS 2, this means I keep the CD player as a transport and can use the DAC in the ND 5 XS 2. That system has a SN2 integrated.
So a combination of CD player with digital output + a streamer is one option and in my case works nicely and keeps the CD player handy if I want to just spin a disc.
Another option for you could be a first generation Uniti with a CD player built in such as a Unitilite, Uniti 2 or from the current Uniti range the Uniti Star.
This would give you a nice one box solution replacing both your CD5i and NAIT XS and adding some nice features like Internet Radio and streaming if your needs took you in that direction. Compared to the NAIT XS based system you have today I’d expect the sound to be comparable and in some cases an improvement, certainly with a Uniti Star which is a very nice product, I almost got one myself to replace my NAIT XS + CD5 XS.
I can’t imagine a DAC-V1 will be a suitable solution, it’s primarily intended as a desktop/computer system having both a USB input (playing music from a computer) as well as an integrated headphone amp and is intended to be paired with a NAP100 power amp to give a flexible and compact desktop system. It also lacks any analogue inputs.
Integrating that sort of system with either a NAIT or CD + Vinyl sources is not what it’s designed for ultimately.
You should find a reasonable quantity of the first generation Uniti integrated products available on the used market, certainly over the last couple of years as owners moved to the current generation of Uniti products that pushed them out for second and third owners to enjoy!
Conclusion, I’d take a radical approach and let your current kit go and replace with a Uniti based system for simplicity given your desire to keep CD and vinyl as your primary sources.
If funds allow you could do a lot worse than the current Uniti Star which has a built in CD player, Analogue inputs for vinyl source and a 70W integrated amplifier giving a nice uplift on what is achievable from your current NAIT XS @ 60W. You also get a very good entry to the world of digital including Internet radio and services like Tidal and Qobuz.