That's the kind of "house rules" I was referring to earlier - dropping weapon vs. armor class, dropping grappling and overbearing, using a different init system, etc. For your 1E games, for example, did you use the init system in the 1E DMG, or a more simplified version a la the 2E init sytem, or like Gary did, just use a 1d10 + dex and casting time mods?
For our games, for instance, we used a 1d10, and used the weapon speed or cast time mod to represent the FASTEST time we could go, rather than as the mod. For instance, if you used a dagger, you could indeed go on a 1 or 2 if you rolled it (subtracting dex mod). If you used a fireball and rolled a 1, and had an 18 DEX, you STILL couldn't go before a "3". And if you used a two-handed sword, you were GOING to go on 10, no matter your roll.

It worked pretty well for us, and kept from having to reconcile what a "17" meant in a round with only 10 segments.