Did the Esoteric CDP have a digital input? If it does then you could try using the DAC in the X-03 with the Vault.
I have to say that going from an Esoteric CDP to the Vault was a curious recommendation on the part of your dealer. It was no doubt motivated by the dealer need to sell the Bluesound. I think that if the X-03 had been functioning, and if you had done side by side comparisons between it and the Vault, the latter would not have fared well. The Vault is a good budget entry into streaming, and I used a Vault 2 for several years , but it usually sounded a bit veiled compared with midfi sources and worse as you ascended the price ladder.
If you saved your CDs, then your question boils down to whether a better transport into the Esoteric DAC can be had. It would be reasonable to start with the old CDP if it can be easily fixed. There were threads here a bit back on the difficulty servicing Esoteric products but they may be easier to fix now. Your dealer should be able to help since he apparently is an Esoteric dealer (and imo he owes you one for conning you on Bluesound.). If it is to much trouble or expense then consider a new dedicated transport to pair with the Esoteric DAC, and it doesn’t have to be an Esoteric