sounds like you'll be getting your hands dirty this weekend!
you may have two or more problems here.
old tired fuel pumps like to stop when they are hot.
fuel pump relays on the other hand will shut you down any-time!
if the pump is loud or howling it's junk!
you can throw your o.v.p. in the trunk and it won't shut you down it will only run like poop!
AS FAR AS LIMP HOME MODE. 88 300E HAD NO SUCH THING.