Well, I'm glad that is sorted out. All our numbers were in agreement but we didn't even know it. What threw me off is (1) when I asked for speed at the gearbox and got speed at the wheel (no biggie) and (2) the 81% number that everyone seemed to know about except me.
Anyway, for the dog, I never meant to imply that all shifting dogs should look like the one 696 made. Heck, we modeled ours after 45 and 968. However, if you are going to do it 45/968/696/etc style (three "fingered" dog) I would suggest keeping it that way and not staggering the dogs fingers on the opposing side.
But yes there are some other ways to do shifting dogs (that don't require CNC) like team 716 style square and pin and hole.
For the size of the shifting dog, what you have looks fine. For the travel, we left a .020 neutral space in ours which worked perfectly. More or less, we made the dog .020 less wide than the space between the dog gears. This allowed enough room to be clear of any potential double engagement (disaster! if it were to happen) but it was small enough that as soon as you were out of one gear you were into the next as soon as the dog fingers aligned with the pockets int he gears. No time wasted in neutral.
Our dog had just under 1/4" of engagement into the gears and worked on 1/2" stroke. We could have probably gotten away with much less but we didn't want to take any chances since it was in the last stage of reduction and behind the power of 3 motors in each box. Teams like 968 run their dogs with about 1/8" of engagement and about .25" of stroke.
In this dog setup you will get a lot of backlash due to the nature of the design. You want the dog pockets in the gears to be wider than the dog fingers on the dog.
We made our dog fingers a straight and easy 60 degrees. We made the pockets only 64 degrees to minimize backlash. It worked well but I wouldn't go with any less than that. You might risk missing a shift if you go smaller than 4 degree difference between the fingers and the pockets. We shifted on about 45 psi usually. A full 60 might have given a faster shift, but we didn't want to apply more side loads than necessary. You might get a little bit quicker shift on maybe a little bit less pressure if you open up the pockets in the gears to 66 degrees but you will get extra backlash.
When drawing your gear pockets and dog pockets/fingers (depending on if you added or removed during extrude) make sure that the lines point to the center of the piece, not just a point on the hex (for the dog). With hours, this was discovered just moments before machining and had to be corrected. You want the lines pointing to the center so you get a flat face-on-face engagement.
Also, I just want to confirm that you do have the dog gears spinning on something. I'm interested in your plans, because everyone does it a little bit different way.
Finally, I think the box can made to be smaller, maybe using smaller gears. I would see what is the minimum gear size you can put between the Chias without having them run into each other. For high gear, it wouldn't make any difference since that initial mating 60 tooth gear has no effect on the high gear speed. For low gear, you'll just want to play with it a bit until you get what you want. That may be a little tricky. I'll think about this some more.
Feel free to use any layout, gear sizes, ratios, etc from this pic
www.team696.org/hexamax_ratios.jpg to help with your design if you'd like.
(Note: In that pic, it is not mentioned that the FP is the 6V model running at 12V and fed through an AM planetary. The 14T gear is on the AM planetary.)
EDIT: Also 4:1 difference between high and low seems like a pretty large jump to me. For the speeds (in fps) you mentioned I think you may find yourself wanting something with more torque than high gear but more speed than low gear when you're on the field. I guess it all depends on the game, but I just wanted to let you know the ratios can be tightened up a bit if desired, something more along the lines of 2.5:1 - 3:1 between high and low.