Picture (s) would help. How much cost savings? Generally, without seeing pics, I prefer lengthwise with house.

1000 sq ft of composite running along the house or perpendicular would cost the same because an 8ft board per ft is the same price as a 16ft board in composite. This is not true with wood. HOWEVER composite boards require more support. Have you factored beefing up the framing to accept the composite? Using mulitple boards to span the width of a houses deck is normal. It does not have to be all one length.

run away from the house so rain water runs OFF the decking.

" We’re redoing an approx 1000 sf deck from wood to composite "

Be careful with a direct replacement as most all composite decking should be on 12" O.C., typical 16" O.C. like for wood. As far as direction, need context for that, post up a pic or two.

The boards need to run perpendiculat to the joists just like any flooring