There are some things which make Burt an attractive candidate as Chris' father - somehow or other.
- Burt takes to Chris early on for no very apparent reason (although there's always the possibility that Burt is simply gay). Chris also seems to take to Burt very easily as a father figure.
- At the end Burt seems strangely content to die with Chris in control of his treasure.
- The marriage issue - Burt has some issues with it (though maybe just because he doesn't want "settled" crew members), and there is a complete absence of any hint that Chris' dad was ever married.
- Chris' narrative stresses that Burt isn't as tall as he is in at least a couple of places - which might fit somehow with the "engineered height" thing.
- Burt is blonde versus Chris dark - but no big deal, particularly with "engineering". Sicilian vs British doesn't have to be a big issue.
- Burt has lots of face hair obscuring his features, and possibly obscuring a resemblance.
In the end, I don't see how it would work. Burt is close to Chris' age, and he does seem really to die at Rio Hato.
Very speculatively, you can also put together a story in which Chris is his own father.
Something like this: Soon after Chris sets off for his trip to the future, Novia tumbles to Ignacio. She's smart, she learns something, maybe she figures out that Ignacio conspired with Lesage; or maybe Ignacio just can't help making a premature move on her.
They fight; Ignacio has to mess her up badly, too badly for 17th century medicine. He takes her and sets off after Chris, whatever he needs to do to follow him to the future, as he did to the past.
They arrive back in 2007 at the same time as the narrator, but unknown to him. By my chronology, the return date is around about the same time as Chris' birth. Call the returned Ignacio "Daddy Chris".
Novia dies; the Chris-foetus is saved (maybe with some "engineering"? Novia is short and maybe a natural Chris will grow up short too. Or something.)
Over the next few years, the narrator does "this and that" & almost lands in jail a couple of times before entering the seminary (presumably to launder his identity and avoid whatever heat is after him). But Daddy Chris takes advantage of having lived through the period already to do better, prospering in the rackets and becoming some kind of executive-level mafioso ...