On one of the blind products that we now produce, we have been following a procedure we were taught by the previous owners of the company. For this process we use Minwax products for the clear coat. And we apply to different parts by both spraying and using a roll coater. We first stain the raw sanded wood, apply SandnSealer, sand and wipe, apply 1 coat of gloss, then 2 coats of satin. We like the product and we like the end result. We do not like that the gloss dry time slows us down and extra day to dry. Here’s my question. The previous owner of the product line said the coat of gloss made the final cured finished look thicker. If the difference between gloss and satin is appearance only, I’m thinking we might as well apply three coats of satin. We will not be burdened with keeping the gloss in inventory, satin dries faster and the procedure becomes simpler. Will the final appearance not be the same? We will test this in the coming days.

There is a world full of better professional products than Minwax. I wouldn't know where to start with a recommendation since there are so many to choose from. I would bet you won't find a single customer that would notice any difference between the product with the gloss and the one without.

The only time I've ever heard of people doing the gloss build coats and a satin/semi final coat would be in bright work on boats. In that case they are doing 5+ coats of expensive very high quality varnish. The idea is if you put on many coats of satin the finish will look cloudy. It's not generally done in the cabinet/woodworking industry. Maybe a piece of furniture by some perfectionist.

As Rich mentioned, Minwax does not make good products. They are all DYI, Consumer products. Generally, oil based that take a long long time to dry. We all switched to Pro grade fast drying solvent & waterborne back in the 2000's. You would be hard pressed to find shops using oil based products. Marine varnish is one of the last.

If I were you, I would spend some time finding a suitable waterborne product line that suits your needs. I personally wouldn't work in a shop with Minwax products. The stench of mineral spirits must be terrible.

Another vote against Minwax. I only use water based 2K's tinted as well as clears, and they are superior to what you're using. I would talk with your hardware distibutor, most of the big guys sell high end finishes as well.

Thanks for the recommendations to look into other products. I certainly agree there are better products out there for certain applications. We do use other waterborne products when we have a spray only situation, or we are producing shutters. We find the results we get with the Minwax is very acceptable and we also see on blind products made in the past that require rework, the Minwax does hold up well on window blinds. One problem we have with switching to other products completely, is we have to have a product that works well when roll coating. In the roll coating type of application, we see some products that spray well, but they don't transfer from the applicator rollers to the wood surfaces evenly and with the desired mils. Of course that might be accomplished with different rollers with a different shore hardness, so for now we prefer to to use the rollers we have, using the Minwax.
I think Rich and Adam have confirmed what I was thinking, and that in our situation there is no benefit to applying a coat of gloss followed by two coats of satin.

Minwax quality aside, there's one other aspect that might be factoring in (but, I doubt it).

Gloss does not have any flattening agent in it, usually this is micro-fine silica. Satin does.

This does produce a very small amount of shading to each coat. I cannot see that one single coat would make a difference however.

Do test this, but test it on your darker colors especially.

Usually when people are doing the gloss undercoat, they do everything in gloss, and do a final topcoat of satin or dull. Most likely, the previous owner tried this and found it lacking in cure time, as you said.

Now, regarding Minwax. If you're using their off-the-shelf oil base polyurethane, there's nothing wrong with it, but I've found Sherwin Williams store brand oil based poly to be easier to work with. You may need to thin it more. I was buying it 15 years ago and it was twice as thick (ie, higher solids) and seemed to cure faster and stronger than Minwax.

Since it's the same basic technology, you might find proper thinning means it works just fine with your roll coater.

The main reason you would apply higher gloss under lower or satin would be for clarity. If you only use the satin it may look more hazy because of the flattening paste in the lower gloss that isn't in the high gloss. But otherwise I'm not sure you are actually seeing that much difference but it may on darker colors.