Get your instructor certs, Champ. AllATPS is good but expensive, and you had better go in ready for it to work in 90 days or whatever they are doing. They are a finishing point, it is not a short cut. I have seen smart people fail because they did not go in ready. Odds are you will fail one or more of the teaching certs anyway no matter where you go, as most people do. Most airlines know this and make allowances, except American Eagle I think.

Here are some things to think about.

Need for a CFI
-------------------------
ATP (see FAR 61.159)
1,500 total time
500 x-cty (>50nm)
100 night
75 combined instrument

Part 135 IFR (see FAR 135.243)
1,200 total time
500 x-cty (point to point)
100 night
75 combined instrument

Need for a CFII
---------------------------
Almost all Part 121 and 135 operators fly approaches all day every day as specified in their ops manuals. You will not even be able to pass sims unless you can fly approaches like a pro. CFII is traditionally how this skill is learned. You also will need that 75 hours minimum instrument time, and to be a pro you may need more than that depending on aptitude.

Need for an MEI
---------------------------
In addition, most everyone hiring for twin engine jobs requires 50 hours and 100 is more common for airlines. The best ones require 200, which suggests you need to have worked somewhere in a twin already before going there, since only rich persons can buy those hours otherwise.

In addition to this, it is my opinion that someone who can explain flying is a better pilot, but I am not in a position to say conclusively. Good luck.