I hope it's not really a blow-up toy LOL. He would shred it and eat it. If it's a stuffed toy, remove button eyes that are sewn on, for he will pull them off and eat them. With other easily pulled off parts do the same.
You say he starts his bite behavior when you stop petting him. He might be just trying to draw you back. Discontinuing the petting might be a good strategy, as long as you can pick him up and put him on the floor for free roaming time.
In general, if he keeps it up, you can't stop this behavior without withholding yourself from him entirely. Your story makes him seem pretty gentle about his love-biting. But with iguanas, with such sharp teeth, even light bites can be damaging. Plus, the behavior can escalate in intensity.
Has he escalated his approach to you? Is he biting harder or faster? Does he do it more often?
IMO, to keep him tame and close, you should try to find some way to closely interact with him. Use a shield, like a dust pan or a fat whisk broom, or possibly better, a real broom, to fend him off when you see the bite behavior start to show. If he escalates his harem gathering behavior by biting hard and fast, or by stalking you, you must not accept that. Keep him in his cage more, and don't sit down with him until this passes.
IMO use just enough force to block his amorous advances, or he may perceive that he needs to escalate to get a shot at you. If you do the visits you describe on a smooth floor, you can push him 20 inches away with a gentle, firm broom push. If the tasting and biting happen on a carpet, watch closely for the start of the taste-and-bite and stand up and move away before he can carry it out.
When you have an interaction time, wear a denim jacket and denim pants with sweat pants pulled over them. Plus sturdy shoes. Also use Kevlar gloves and forearm sleeves. They are inexpensive, and your ig can't bite through them, since he does not have peg-like teeth. Believe it or not, he can shear through the leather of work gloves.
You won't know he'd ever bite your hand, arm, or face until the first time he does it. In your place I would prepare for that by gloving-up for every handling session. Do not lean over close to him. If/when he bites you there, you will be glad for your armor.
I don't have good internet access, so I can't give you examples of gloves and sleeves. I used to use knitted Kevlar yarn gloves that had strands of stainless steel woven in. They are still available, and are not expensive. Get them if you can. Kevlar sleeves for protecting your forearms have thumb-holes. You put the gloves on first, then put on the sleeves, sliding your thumb through the hole. The Kevlar woven gloves with rubber dots on the palms and fingers give you more control when you are handling your iguana.
Check these one piece hand-and-arm gloves, which are the only example I can look up:
Magid CutMaster Knit Glove, Attached 24" Kevlar Sleeve, Made with DupontŪ KevlarŪ 1000
The address is far too long to post it here.