My suggestion would be to do like they have with contract negotiations: With each change to an offer, the morale of the GM drops, with him demanding more or cancelling the trade outright if you keep moving the goalposts.
Have an undisplayed relationship rating that affects your ability to trade with each team (or use the smiley icon). If you renegotiate too many deals or bug him with too many unrealistic deals ("Will you trade Mike Trout for Dylan Moore?") the relationship rating drops, making him less likely to respond to your player shops or to accept your more reasonable deals.
Leaving the guy alone for awhile or getting a less favorable trade accepted could raise the rating a bit (on the theory that he's more likely to want to deal with you if he knows he can win the deal).
This could make the trade AI work a little better by making it more difficult for you to win a deal by adding to it after it's accepted. If your initial deal is accepted, then that's what you've got.
"I'm offering Abraham Toro for David Fletcher".
"Let's Do It."
"How about Abraham Toro for David Fletcher and Jo Adell?"
"No."
"Abraham Toro for David Fletcher and Kean Wong?"
"Not a chance."
"Abraham Toro for David Fletcher and Jaime Birria?"
"I'm hanging up now. Leave me alone!"
"Abraham Toro for David Fletcher?"
The Angels GM refuses to deal with you at this time.