Install Tankless water heater in the cold line
I really don't understand your proposal but if you're adamant about it then just supplement your hot line with a tankless closer to your fixtures. If you set your tank to 125F and your tankless to 120F then your tankless should only operate for a very short period instead of always warming the incoming cold line. If your tank ever runs out then your tankless will pick up the slack.

Better yet, relocate your water heater closer to your fixtures; this would save you thousands as average cost for tankless install is $4,000.

I see your proposal has a third line going from the tankless to your fixtures but fixtures don't accept a third line. You would have to junction it into one of the lines (presumably the hot) right before the fixture. Even if you junction into a hot line it will be a mix of hot (tankless) plus cold (tank) at the hot tap until both lines are full of hot water so this would actually increase the total wait time for hot water at the tap.
One thing you cannot overlook is that tankless units are typically 200,000 BTU/HR and typical residential natural gas can supply about 225,000 BTU/HR so a gas upgrade will probably be required.