Subfloor repair question

Hello,
I'm in the midst of a bathroom remodel on my 1910 house, thanks to everyone for their responses to my previous queries. I had to repair some water damage to the subfloor, and before I cover it up with 3/8" underlayment for natural linoleum, I have a couple questions.
The original subfloor is 7/8" thick tongue and groove 1x4s, and my floor joists are 16" on center. I found some 7/8" thick plywood and made my repairs by cutting back the damaged areas of the subfloor to the midline of the joists. So:
1) What sort of support at the butt seams perpendicular to the joists is appropriate? I put blocking between the joists on the boundary of the largest repair, but that was a a fair amount of trouble. For the other areas, should I attach some strapping to the underside of the new and old subfloor? E.g. some 1/2" plywood 4" wide parallel to the seam, nailed from below with 3d nails.
2) In a few places I didn't makes my cuts perfectly straight, and as a results there are gaps at the seams of up to 1/8" where I can see light from the crawl space. Maybe I'm being picky, but I'd like to fill these gaps. What is an appropriate product to use? I thought of the expanding urethane foam gap sealer, but I'd prefer something that expands less and is heftier.
Thanks, Wayne
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<< For the other areas, should I attach some strapping to the underside of the new and old subfloor? E.g. some 1/2" plywood 4" wide parallel to the seam, nailed from below with 3d nails. >>
Use plywood with a good dollop of consruction adhesive, nailed just enough to keep it in place until the adhesives sets.
<< there are gaps at the seams of up to 1/8" where I can see light from the crawl space I'd like to fill these gaps. What is an appropriate product to use? >>
Bondo is used a lot. It sets fast, adheres well and is easy to sand level.
HTH
Joe
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