Or: If Axel had approuched the situation as an Asasin, not a friend.
Summary: Yes, Axel could have taken his cannon approuch. In another life, he could totally see himself doing that. In this one, he's alot more proactive.

Yes, Axel could have continued trying to convince Roxas to come. Or, failing that, just jogged his memory, and left (leaving DIZ and the Organization in the dust), which Axel would have been okay with. Not great (they would be hunted down by both sides), but it would have been dealable (much more than never seeing Roxas again). However...
It just wasn't working.
The Organization was impatient. More willing to get rid of Roxas, and start over than give him a CHANCE. Whatever memories DIZ gave him were working- Roxas was way too attached to his data-friends to just LEAVE-and why would he? Axel was the stranger, the wierd guy in a black-coat. Axel couldn't blame him, if he was in Roxas' shoes, he wouldn't trust himself either.
And really, Roxas was going through alot. To him, he was just minding his own business, a normal, ordinary life, when the world suddenly stopped making sense. He must think he's going crazy- with the timestops, poeple no one else seeing, fighting monsters. It was an explination about how the universe must look, if people weren't introduced after having their world destroyed by monsters. Unbelievable, but happening so quickly, that no one could deny it. Roxas, could, since he was the only one noticing it.
So now, Axel had to (somehow) explain the situation (which sounded completely ludercruis), without looking like a badguy. Along with other, even less fun stuff, like 'what is going on?', 'who are you people?', 'what are those wierd, white creatures?', and Axel's personal favorite (NOT) 'whatdya mean were best-friends?!'. And quickly/quietly, otherwise DIZ would notice, and intervene again...yeah, not happening.
In another life, he could see himself doing that, anyway. Because, Roxas was worth the effort, even if it was hopeless.
In this one, Axel remembered one cruical fact.
Axel was the Organizations Asasin. Yes, he had colored it to Roxas, but the job included being SMART with a side of ruthless. Getting close to someone, so you could betray them later. Poisons, and eliminating a target in their sleep. Inflitration, and theft, and grave-making, and romantic rondevus with bad intentions, and so-so-many backstage, ninja stuff. That Roxas was NEVER allowed to know. Because Roxas would never accept the worst of the Organization, was too good-too Light, and if he did-he wouldn't be Roxas (Roxas looking at him, eyes bright with confusion and betrayal, with I-Though-You-Were-Better-Than-This.) If Roxas knew, he would never come back to the Organization (Axel), memories or not. Some of the stuff they did turned Axel's stomache, and Castle Oblivion was positively low-key in comparison to his usual jobs (mostly because his usual method would've left Axel a suspect).
Oh, how he hated the icky jobs.
But, they helped develope alot of useful skills. Like, how to stalk someone and break into a house, while avoiding varios watchers.
Axel was fairly familar with Roxas' scedual. Wake up, meet his friends, do something, say hi to everyone in the niehborhood, go home, restart. He had spent the entire mission doing recon (stalking) the blond (trying to forget his problems). He knew when Roxas would be coming home, and about the time the zombie would be asleep.
And, more importantly, when Riku and the crew would be the least likely to be paying attention. With no witnesses (digital or otherwise) to make it messy.
Ordinarily, Axel would never dream of trying anything this underhanded. Not against his friend-he respected Roxas too much. And, he was kinda weariy, about how the Organization would treat Roxas, they were acting sorta suspious. It was easier to let someone escape, in a non-suspious way, by throwing a fight. However...
Roxas didn't remember him (that hurt). And whatever DIZ wanted couldn't be that different from the Organization.
It was so much simplier to push a sleeping Roxas into a Corridor. Yeah, he woke up- but you try putting up a fight at midnight, half-asleep, with your only warning being pushed off your bed, into a Corridor.
Axel would explain, later.