The basic requirements for minimum conditions (which appears to be your concern) -
(a) Vmcg can't be less than Vef, rather than V1.
(b) so far as the NW load and NWS is concerned, the certification testing avoids both.
(c) CG max aft and, usually, minimum weight.
(d) XW nil
The problem is that, if you are playing in the real world near Vmcg, generally you aren't going to be replicating the certification requirements so it gets a bit rubbery. Be very aware that the directional control animal gets very aggressive, VERY rapidly, in the last few knots as the speed reduces toward Vmcg - the certification Vmcg flight test stuff potentially is REALLY hazardous.
A significant adverse problem is crosswind. If from the failed side of the house, the "real world Vmcg" (as opposed to the book figure) will go up. This delta can be quite significant and, for a 744, you might be looking at something in excess of 1kt/kt. In the case of a stiff crosswind, a takeoff with a planned min V1 schedule is something which one probably should try and avoid unless the V1 can be increased by an appropriate margin to avoid the XW concerns.
So, the short answer, generally, is that you ought not need to push the stick forward, but it is going to help the situation for the real world pilot, so it fits the bill as a "good idea". Forget centreline tracking ... that just isn't going to happen. I have archived video of some DC9 work we did (TP is a PPRuNer) and, as the runway head cameraman, it was quite illustrative to see just how the DC9 (said by just about every DC9 pilot to be an aircraft on rails with a failure) promptly leaped out of the viewfinder ... except for the wingtip. The aircraft will yaw, deviate and then, if things go well, either parallel or, maybe, come back towards the centreline a tad, prior to lift off. There is no specific requirement for either of these to occur and one could well see the deviation limited by the liftoff. Generally, the continued takeoff is the critical situation as, in a reject case, the throttles will be closed in short order.
Have a read of the flight test things at page 111 of
AC 25-7C Flight Test Guide For Certification Of Transport Category Airplanes (faa.gov)
The current rulebook requirement is at FAR 25.149(e) - see
Electronic Code of Federal Regulations (eCFR)
You would need to do some homework to see if the 744 met these requirements or something earlier and, perhaps, a little different. I'll leave that for your spare time ...