When you apply multiple coats of urethane, any dust or small flaws will be amplified with each new coat. If you want the smoothest finish possible, then wait until it is dry, very lightly sand with very fine paper (220 or finer) to remove any dust bumps, wipe it clean with a slightly damp cloth or tact rag, let it dry or buff it dry with a dry cloth, then apply the next coat. There is no reason to use mineral spirits, actually I would advise you not to use mineral spirits.
I see no advantage to applying successive coats with, then against the grain. As long as you apply an even coat with a good quality brush or foam brush and don't overwork it, any brush marks should disappear. The finished product should be so smooth that you couldn't tell which way you brushed the urethane on. Also, if you are using a satin finish urethane, be sure to mix it well, stirred, not shaken. The dulling agents tend to fall to the bottom, so it is important to mix it well. No matter how many coats you apply, it should not become "glossy".
Spray foam insulation for large areas with a closed-cell foam tends to be a job performed by professionals. They will mask off the area being sprayed, and bring in a bunch of specialized equipment to do the job fast. The result doesn't require a separate vapor barrier since closed cell foam is a barrier. It does have the downside that any future repairs or renovations will require a significant effort to remove the foam.
The main reason to spray foam an attic space is to make the area a living space and eliminate the need to ventilate under the roof (typically done to prevent ice dams). To do this, they would spray directly under the roof, between the rafters, rather than between the joists. Otherwise, the traditional solutions are blown and fiberglass insulation.
Blown insulation requires the vapor barrier to be put down first, soffits to be protected so they aren't covered over, and then a machine can be rented to blow in as much insulation as you like. The advantage of blown insulation is speed, fewer gaps in the insulation, and it's easy to add a few extra inches. If you ever need to remove a ceiling under blown insulation, it becomes difficult since you first need to remove all the insulation unless you want it falling into the room below.
With fiberglass insulation, the vapor barrier is often attached, but it needs to be stapled to the joists, which is difficult to do from above. It's much easier to temporarily move out of the way for a repair or renovation, but it's also easy to leave small cracks where moisture and heat can escape.
If your problem was that you had wind blown rain entering from your soffits, then you may need to add a baffle or some other storm resistant vent that blocks the wind driven rain while still providing fresh air all other times.
![soffit baffle](https://i.stack.imgur.com/CobAt.jpg)
Best Answer
I add 20% thinner to my polyurethane to promote even coats, prevent bubbles(they pop more easily on their own when thin), and speed up drying time. You can alternatively use lacquer thinner and this will dry even more quickly due to it's lower flash point -- but in high temperatures it might dry too quickly.
As far as methodology for mixing, I have a "mixing can" that I bought at a big box store -- they sell empty paint cans -- and I add 20% thinner and the rest poly. I use a plastic can attachment that acts as a spout to prevent poly from filling the lid gap when pouring. Stir with a stir stick. I don't get too many bubbles but I don't worry about them either because they pop on their own. Pour onto the side of the can to prevent bubbles (think of pouring beer from a bottle into a glass).