That's gonna be a tough nut to crack considering you probably need to rigorously modify the thing on microchip levels

Marshall Echohead EH-1 does spillover and is cheap. Zoom MS-50G Multistomp also does spillover and has possibility to add other effects on the chain for boost and EQ.

I guess I will be buying a new delay soon.

For $99, you can grab ProGuitarShop's vintage voiced take on the Flashback, the Alter Ego. That's $70 less than the standard Flashback.

I have a regular Flashback & the Alter Ego X4. Really dig the vintage style delays. Plus you still have the Toneprint slot (on the Alter Ego) should you want to load up modern sounding delays

http://proguitarshop.com/tc-electronic-alter-ego-2.html

My eventide timefactor does spillover, but they are not cheap