The timing rule under RESPA is based on the rule that one of the lenders -- the originating lender -- must be subject to RESPA. A lender cannot evade RESPA coverage by structuring table funding. It sounds as though you are setting up a clear procedure that makes your institution the lender for purposes of RESPA. You are the funding lender and therefor make the original disclosures (HUD-1, etc.) It makes no difference for purposes of RESPA whether you keep the loan for 1 month, 1 day, 1 hour, or 1 minute. State law may have something different to say.
As for disclosures, as the original lender, you are obligated on all lending disclosures (appraisal notice, flood determination, TIL, and the RESPA stuff.) Servicing transfer can actually be handled by giving the transfer "good-bye" notice at closing. That way the borrower is clear and you know that the borrower received it.
The escrow notice is an interesting issue. The lender actually has 45 days to deliver the initial escrow notice. The lender also owes the borrower a close-out short-year escrow notice when the servicing is transferred. However, it sounds as though you are not actually setting up the escrow notice -- the purchaser is. If that is the case, you only need disclose the information that is pertinent to closing -- the funds you are collecting to put into the escrow account that the purchaser will set up.