I do not recall that at all, Speed Factors only effected initiative in 2nd Ed, I thought.
But, unfortunately, it seems, I have yet to have a definite answer on multiple attacks and moving in pre-3rd Ed.
I'm not THE EXPERT, and I could be wrong but...
1E initiative becomes... intricate. Speed Factors in 1E affected your initiative but not in necessarily simple ways because determining who goes first wasn't always just a plain, straight-up, who-rolled-higher check. When combat was limited to just melee attacks it was easy to determine, but introducing missile fire and spellcasting muddied things tremendously. The best way to understand it is to do a search for and use A.D.D.I.C.T. by DMPrata. People still argue some of the points - and in fact they will never, EVER be unconditionally resolved - but he pretty much gets the as-written system broken down into a procedure that can be clearly understood and reliably followed.
1E certainly didn't ever subdivide your ability to make all your attacks and move your movement. Unless, as already mentioned, you were more than 1" from your opponents (which then required either charging or wasting a round closing the distance) you were free to move your standard movement as well as take all of your attacks.
As also mentioned, when PC's have multiple attacks the timing is made more complicated with attacks beyond your first either coming at the end of the round or woven in between the opponents mulitple attacks. It also makes a difference as to how you are GETTING those mulitple attacks. If it was part of your "attack routine" that's different than if it's a bonus or extra attack such as enabled by a haste spell.
There's lots of reasons why 1E intiative is so messed up and why EGG himself didn't use it. Mostly I think it comes down to the fact that at THAT time combat was percieved MUCH differently than it is now. How combat was run by DM's and WHY it was run that way... well, it just doesn't happen that way anymore. DM's had a LOT more leeway in determining arbitrarily how the game at their table was going to work and they had few or no hesitations in exercising that privilege.
Don't have 2E books to easily consult anymore but it greatly simplified the initiative process. Maybe even too much. It did reduce it to a simple, straight-up comparison of initiative roll results. You rolled the initiative die, added a modifier or two from a short list and the SIDE with the lowest roll went first, took their standard movement, made all their attacks, and then the losing side did the same. I don't recall even reading anything about needing to interpolate multiple attacks or restrict movement when making mulitple attacks (or restrict attacks when taking full movement).
2E then also had OPTIONAL methods which I think were used so often that they were frequently perceived as the default - individual initiative, more modifiers, Weapon Speed Factors, spell casting times, etc. But it was still allowing a character to take their full movement, plus all their attacks, and all on their own turn, not waiting for the end of the round or somesuch before resolving things. But I still don't recall anything about having to limit your movement or number of attacks in order to both move and "full attack" in the same round. If it did it would have been a strictly optional initiative rule.