Yes, try using the same weight first. And yes, try using the same arrow. You'll probably find traditional equipement is much more tolerant then a compound.

You can use adapters to match heads like zwickey which are made for a tapered wooded shaft with your aluminum arrows. Only problem is that they'll add a bunch of weight. I believe you can get a coc by magnus with the adapters already installed in 125 grain. My problem with them though is that the adapter is rather small and weak compared to the regular long adapter.

Personally, I'd look to stingers or phantoms.