You may be dead on......... Honda cranks have a thin outer shield/cover and I'm unsure WHY they made them that way?? Maybe if I buy a junk one and cut it up, I'd understand it. They may drill and balance them under that shield and the shield just keeps the atomized fuel mix flowing smooth over those thin covers?? I'm not sure but any good crank/' performance engine builder would know..........
Cranks are not cheap - about 350$ even from a discounted retailer such as Service Honda. But, if you HAVE the $$, you'll have peace of mind for a decade and longer to come.......
I have DEEPA's old 85 crank here and it's out of true. I tried my best but could not get it in spec. He ran it a year (as it was) with no issue but I was certainly unhappy with it!
I'm SURE that I was more worried than he was 
Are you sure the side to side play is too much? You have to read the Shop service manual and check the spec with a feeler gauge...... Lots of guys think there crank is junk do to the side play but it's the up/down play that is usually noticeable along with the side to side big end bearing clearances. They all have side to side play; Just think about your "small end" or where it rides within the piston and on the wrist pin. There's a TON of slop up there! but it must be necessary for whatever reason......
We opted for the spacer plate and brand new "long rod" crank and I bet it won't be apart again for YEARS!
People are STILL running there stock cranks with nothing more than the main bearings being changed ever so often; They seem to hold up dam well !!
Some shops change the rod for 80$ -120$ or so plus parts which is very reasonable seeing that it has to be trued up and done perfectly.
I'll NEVER claim to be a crank "specialist"
All our government does is distract us while they steal from us, misspend our tax $ and ruin our country