I think using Phoenix splice in + Deezy loop out service would be cheaper
You send onchain sats from cex to Phoenix, then use Deezy, Fixedfloat, Boltz or whatever depend on the lowest cost you can found
Cost breakdown : Emergency onchain tx fee ( splice in when using Phoenix ) Also extra 1.000 sats for "first time fee" Sending from Phoenix to the loop out service would cost 0.4% Then use whatever Loop out service you prefer
Just my 2 sats
I have been thinking about a similar approach to this as you describe above. An additional step you can take -- If you really want to reduce trust in any one LSP -- is to do a few hops. From Phoenix --> Breez --> Blixt --> <your preferred/cheapest loop-out option>.
A particularly compelling instance is if your KYC'd exchange offers LN withdrawals. The majority of centralized exchanges operate account-based systems for users, and so UTXOs are only "created" (associated with users) in an on-chain withdrawal. Thus, leveraging the LN withdrawal + multiple hop method obfuscates a user's future activity from all but the final LSP.
One or many LSPs need to have some level of trust in this strategy, but at least the user can determine that.