The combat system works just fine, no worries there. Where I run into problems is saving throws.
Part of the reason for this little exercise was to remove the use of any dice but d6's from the purview of the players--only the DM will roll % dice, d4, d8, d12, etc., and then only for checking charts and probabilities (surprise, etc.)
This leaves us with the problem of the Saving Throw. Saving throws, as laid out in Men and Magic, are made with a d20, with no alternate system referenced.
...at least, not explicitly. But there is, in fact, a saving throw system in Chainmail. On page 31 of Chainmail we see the necessary rolls on 2d6 to "Save" a figure from a Wizard's missiles. Can we, then, extrapolate from this to work out a 2d6 Save system for OD&D?
I believe we can.
Chainmail has Heroes and Super Heroes being saved on a roll of 9 and 6 or better, respectively. if Heroes are 4th level Fighting Men, and Super Heroes 8th, let's see if we can work this out.
The first thing we need to do is accept two things: first, we are replacing save categories with a single saving throw. I have no issue with this, as I'm all about keeping things simple. We'll get into optional adjustments for categories in a minute. The second is that this is not likely to be a linear progression. Again, I have little problem with this, because it's believable that the better someone gets at something, the fewer broad leaps forward they take, and the more improvement becomes smaller increments. One who is already an expert savant rarely makes the kind of great intuitive leaps of learning that a novice or even journeyman does. Skills and abilities generally hit a plateau somewhere.
Thus, I come up with the following. This system makes it much harder to save at low levels than does the d20-based one in Men & Magic, but likely much easier at higher levels.
This table applies to Fighting Men only. As with OD&D, Magic-Users should progress in increments of 6, Clerics in increments of 5. Now, I've always liked the idea that Thieves are lucky, so I'm going to give them saves as Fighting Men, just for fun.
Fighting Men includes Paladins and Rangers as well as Thieves and Assassins.
Magic-Users includes Illusionists (we'll get there, don't worry!)
Clerics includes Monks, Druids, and Bards.
Option: Save Categories
This might overcomplicate things a bit, so I'm torn on whether to include it. M&M, of course, includes the ever popular categories of save: Death Ray/Poison, Wands, Petrification, Dragon Breath, Staves and Spells. Since our new chart has only one save, it's possible to simulate these categories with bonuses to the save. If we assume a base save of 16 (as this is the worst save on the level one charts in M&M), we can assign bonuses by class as follows:
This table is not an exact translation from M&M; that would be nearly impossible. I instead estimated bonuses based on the difference between the M&M save and 16, divided by 2 (since our range of possibilities is nearly half that of a d20). I went with my gut on rounding off fractions up or down, and made one alteration, giving Magic Users a higher bonus against spells.
Using this system, a roll of 2 on 2d6 would always fail a save, regardless of bonuses. Come to think of it, this probably wouldn't complicate matters much at all, so long as the players kept their bonuses written on their character cards...
Anyway, there you have it: a Saving Throw system derived from Chainmail.