And he's still trying to split the difference:
I also support exemptions to background check procedures for certain situations. Current legislation under consideration would not require a background check and explicitly allow for gifts between family members, for licensed hunting or sporting purposes, and for transfers in legal wills. This legislation also reaffirms the long-established prohibition on any system for the registration of firearms and records of a transfer.
It's best to drop him a line. On the upside it does show that the bills are being watered down (which is a negotiating tactic on their part as they try to gin up votes.
I'd wonder if he would really vote against a bill that would maintain records as the rest of his Party is eager to do.
And note that the ACLU itself is against these bills for this exact reason.