I'm confident you will get better overall performance out of the Eico ST-40 output transformers than the Hammond 1620. In stock form, the Heathkit adds I think about 20 dB of global negative feedback. How much feedback you can add depends on the quality of the output transformers. Can you get to the stock 20 dB GNFB level with the Eico ST-40's in the Heathkit W5M circuit? Not sure, but I think you will have a much better go at it over any 16xx-line Hammond output transformer. Also be aware the 1620 uses what I will call their "traditional" secondary winding method. That means the secondary is not one continuous winding with taps at 8 and 4 ohms. With the traditional Hammond secondary winding method, you get either 16 ohms, OR 8 and 4 ohms, but not all three simultaneously.
What I can say about the traditional Hammond secondary winding approach is they produce stellar LF response, but you need to make some fairly serious compromises on amplifier transient tuning to squeak out reasonable performance in the HF. Typically you would not want to add more than say 10 to 12 dB of GNFB with their traditional winding secondaries so that you stay away from the HF shortcomings of these transformers.
On the other hand if you are talking about the new "A" winding method of the Hammond secondaries (e.g., the 1620A in this case), then it does use one continuous 16 ohm wind with taps at 4 and 8 ohms. I have zero experience with the "A" secondary winding method from Hammond...maybe others do, and these might be okay.
Of course, you could purchase an old stock set of 16309's. They do come up for sale from time to time on the auction site. It might take you 6 to 12 months to source a pair though. The W5M is a very capable amplifier when properly restored/tuned, so I would say use the best iron you can find, and I think there are better choices than Hammond for the Heathkit W5M.