A 5/8" ID/1 3/8" sealed bearing should be very easy to find.
If uncomfortable, increase the plate size, say, from 1/8" to 3/16"/1/4".
This might be part of what you're looking for:
and this:
If you can't find the correct size bearing, use this:
or this:
Your motor mount plate should be ok, especially if it's welded to the frame.I thought about that. The bearing pillows I have mount pretty well to the engine mount, but I don't feel too comfortable with messing with that piece.
If uncomfortable, increase the plate size, say, from 1/8" to 3/16"/1/4".
This might be part of what you're looking for:
and this:

FICTION SAVAGE SEALED MID BOTTOM BRACKET 19MM BMX BIKE BB KIT FIT CULT PRIMO | eBay
New Fiction Savage MID Sealed Bottom Bracket Kit 19MM IN BLACK, SILVER, RED OR BLUE. LISTED PRICE IS FOR ONE BOTTOM BRACKET KIT. To many issues sorry.
www.ebay.com
If you can't find the correct size bearing, use this:

5/8" x 3/4" x 3" Shaft Adapter Pulley Bore Reducer Sleeve Bushing Sheave Key | eBay
Find many great new & used options and get the best deals for 5/8" x 3/4" x 3" Shaft Adapter Pulley Bore Reducer Sleeve Bushing Sheave Key at the best online prices at eBay! Free shipping for many products!
www.ebay.com
or this:
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