I'm not going to call you names or try to tell you that your theory is stupid, but I see a lot of problems with it. Please note this is show only. Something else could happen in the books, but I agree with Stannis Lives that I really don't think that GRRM would be so "disingenuous."
Not all babies are born covered in blood. Some come out looking totally normal. Even if he was soaked in blood, someone wrapped him up. Obviously they cleaned him up with one of the many, many bloody towels laying around the room. His cleanliness is hardly evidence.
If Lyanna didn't birth him, who did? One of the nurses standing there? 99.99 percent of women can't stand up for hours after they give birth. Is there some random postpartum woman hiding deep within the TOJ?
But, no, you think the child is Rhaegar and Elia's. So where is Elia? When did she give birth? Having Rhaenys almost killed her, and after Aegon the Maesters aid she wouldn't have any more children. Rhaegar left Elia at Dragonstone and ran off with Lyanna, then Elia was a prisoner at KL. When would Rhaegar have impregnated her? Wouldn't someone have noticed that she was pregnant? The baby at the TOJ can't be Aegon. Aegon would be about 18 months old by then.So I just don't get that.How did she get back to KL to be raped and murdered. It's not Elia's baby. For a hundred reasons.
JonCon isn't in the show, and I don't think he will be. So whatever he knew/saw/says/does doesn't really matter.
In the scene, there's a blanket or something over Lyanna's stomach. Possibly covering up the massively botched C section performed with a dagger? That would explain the blood everywhere. Come on, man. She had a baby.
But let's just say that someone stabbed Lyanna. Who? Why? Why would nurses be attending her, and Kingsguard protecting her, just so she could die slowly? The only person/people who would want her dead would be Elia or the Martells. But again, Kingsguard. I don't see how that could happen. Rhaegar left her there with help and protection so she could birth their child. Unless the Kingsguard killed her, which WHY, and wouldn't she say ARTHUR DAYNE STABBED ME A LOT AND FORCED ME TO GIVE YOU THIS BABY?
If the baby wasn't Lyanna's, why was she so concerned about his safety? Why would she burden Ned with him if he wasn't half Stark? Why would Robert be so enraged if he wasn't hers? I guess Robert would want to murder any Targaryen, but he would want to super-kill that one.
If the dragon has three heads, and they are Dany, Jon, and Tyrion, then they all share the special distinction of killing their mothers during birth. Yes, including Jon, son of Lyanna.
If anything, Rhaegar may not be the father. Aerys may be the father of all three of them.
But let's just say it is Rhaegar, because it is, and talk about your tagline: "No matter how many times you say it, bastards can't inherit the Iron Throne in Westeros." IF Rhaegar married Lyanna, which is possible since he's a Targ, Jon isn't a bastard. Especially if he was born after Elia died. And 2 bastards have already inherited the Iron Throne. And I don't think that the IT is Jon's ambition or destiny anyway.
I respect your dedication to your theory, or rather your dogged disbelief in the R+L=J theory, but it's just really hard to justify. Like, damn near impossible to explain.