Ok, here's my suggestion again:
Have your coin buttons hooked up normally. Map MAME so Start 1 is P1B1 (L Ctrl) Start 2 is P2B1 (A), Start 3 is P3B1, and Start 4 is P4B1. Either leave off the Start buttons or include them and wire them in parallel with the appropriate player's button 1 buttons as shown above.
I tried several games as well as asking on the MAME forum and only found the following drawbacks: (If anyone finds a game that has problems with this, please let me know by posting here).
These are ordered from least severe to most severe.
If you press Start in the middle of a game, the P1B1 action will occur, but I can't think of when you would ever do this.
If you coin-up a game and accidentally press P1Button1, the game will start, but you are not likely to do this.
If you are playing a game, have a bunch of credits racked up, and accidentally hit P1Button1 after you die, you will continue playing the game and have to suicide to end your turn.
A few games (1942, Arknoid2, gng, for sure but there may be others) were looking for you to press and hold Fire and then press Start to continue. For these games, pressing either Fire or Start will immediately continue. (I prefer this, actually, but it's not arcade accurate).
A few games (Rastan for sure, but there may be others), would allow you to press Start to continue, or Player 1 Button 1 to stop the counter and start a new game. For these games, pressing Start or P1B1 will continue and you will have to wait the full 10 seconds before starting a new game without continuing.
One game (Primal Rage, but there may be others) uses the Start button as an attack button, but it is not the same as P1Button 1. For this game, P1Button1 would have to be re-mapped, and the keyboard layout might be less than ideal, but this method will still work.
The problems are less severe than they sound, if you actually try it out. (This is a way to get four additional inputs out of your keyboard encoder).