Planters, in the paper I sent you, they estimated an 11 micron Pump Spot size.. If you can hit that, I think its doable. Dye lasers have been pumped with a few 10s of mW of HeNe, lasing in the near IR. The record is a threshold with something like 5 mW of red HENE pump, with a very high gain IR dye... Hene's advantage, as well as Argon, was the small spot size with a pure TEM00 beam. Plus we have much better coatings now then in the 80s...
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Our friend at Joss Research thresholded a 599 Ring Dye at ~ 2 watts of DPSS 532 Green multimode pump a while back. I had sent him the optics that were missing from the dye laser head... If he had pump power way above threshold, he might have got it aligned better, been able to toy with the mixture, and brought that threshold way down, while increasing lasing output... He did that with a less then optimal water based dye.
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Since you have that six Watt tight green, I'd start there, get the cavity lasing, and work your way through the compressing optics for the diode later.. I'll see what I have in the dye optics pile, Lord knows I'll never use them at this rate.
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Steve
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When I still could have...