If you don't have the right tools and techniques you will get lousy cuts and blown out veneers on one side or both.
Straight cuts and curve cuts require different tools.
Having had a wood shop I had access to all the right tools, equipment
and technique. My advice would be as follows, but if you provide more information about your situation a procedure which better fits YOUR circumstances can be outlined:
Use some stiff cardboard or very thin plywood
which is flat and make templates of the entire job, labeling each mating edge and which is the side to be facing uo. Hopefully most of the cuts can be straight and parallel.
For those cuts that aren't you can still cut a rectangular piece and use the template to trace the non parallel or curved cut and even cut it oversized and use a belt sander to remove the excess material to the line.
You will want the grain running through effectively making your cuts like those in a jig saw so that it is not ONLY shape and size that matters but pattern.
With the inlaid strips this means a lot of planning so that you have no cuts too close to the small ash strips or right down one.
Layout is more important than the actual cutting.
You might consider working out the entire cut schedule including the sequence of the cuts and bring it all to a wood shop and pay them to cut it with there machinery.. hopefully as you stand by. If not make sure they understand the job thoroughly.
If you mill the panels
yourself with hand power saws you will want to clamp on a straight edge and not try to cut a straight line even by following a drawn line.
Do some practice cuts on sacrificial material to determine the exact distance to clamp the fence guide.
All milling and cutting and sanding
and tooling should be INTO the face of the good side... this means the teeth cute down. If you must use a reciprocating saw, use a very fine tooth blade and make sure that the teeth have the correct orientation. You can get reverse toothed blades.
Applying tape to the surface my reduce splintering for poor cutting tools, but it is always better to use the proper shape carbide tipped blades. And ATB tooth is fine for expensive plywood
veneer. You will also want to have a blade with the correct number of teeth per inch. *0 teeth would be fine for a 10" blade.
Make some practice cuts on some sacrificial material and work everything out. You only get one chance at that expensive veneer wood.. so plan plan plan ahead.
You also might want to prefinish the panel BEFORE you cut it. You can over coat and do the edges and backside after.