Thin wall tubes? And no grooves, use small serrations.
If the tubes are heavy wall switch to 2205 tubesheet.
It can be done but the rolling window is very tight, slightest over-roll and they will leak, and nearly no chance to re-roll.
Of just roll to contact and then seal weld.
I agree with Tinman, chasing leaks will cost a lot more than changing tubesheets.
Today 316 and 2205 are close in price. Suck it up and do it right.
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P.E. Metallurgy, Plymouth Tube