What is the most cost effective way of combining an instrument and multi engine check ride?
The cheapest way (I'm talking Canada here) is to do the basic instrument training in the single, then do the multi rating and check ride separately, then the do some practice approaches and emergencies in the twin and multi simulator to prepare for the multi-IFR checkride , and do that.  There's no point in doing an SE check ride.  When I did it some years ago I bit the bullet and did almost of the air time in a Seminole because I was uncomfortable with going into a multi-IFR checkride with maybe only 15 hours in the twin, and the kind of sims available today didn't exist.

Go to a school that has one of those Red Bird motion simulators or equivalent and take maximum advantage of the portion of the training that can be in a sim.  That'll save a ton of money.

Also use MS Flight Sim or Xplane to practice practice practice at home.  It is a very powerful tool if used properly.  By "properly" I man make sure the stuff you practice on your own is being correctly done, and are not reinforcing incorrect stuff.