What wire is needed for a 400 Amp service between the mast and the meter?

First off, the utility generally makes the hookups at the service masthead

The first order of business is a point of clarification. According to what I have been able to find, your utility is conventional in that they make the final connection from the service drop to the service entrance conductors coming out of the weatherhead; the 18" tails are required so the linesperson can make those splices comfortably.

As to sizing...

This leaves us with mast and conduit sizing. A 3" rigid (galvanized) conduit mast is generally considered adequate for a 400A service entrance, at least from the utility service requirements I have read, as physical strength is also a factor here, not just conduit fill (although a smaller conduit wouldn't work anyway, as you'll see below, due to the need to upsize the wires).

This brings us to wire sizing, which is a bit non-intuitive as parallel wires still need to have their ampacities derated for fill as per NEC 310.15(B)(3)(a), but we also have to apply the 83% demand factor for residential services provided by 310.15(B)(7) point 1. Furthermore, meter socket lugs aren't rated for 90°C, so we have to use the 75°C column instead. This means your 4/0 is right out as two 4/0 wires in parallel can't even get us to 400A to begin with before we apply the derating.

So, we must upsize the wire. While 250kcmil seems like an attractive next stop, and two 250kcmil wires in parallel can manage 410A on 75°C terminations, we have to take 20% off the top to account for the fact there are 6 wires in the conduit. This puts us down at 328A for the parallel combination, just short of the 332A required by the 83% rule for a 400A nominal service entrance.

As a result, we find ourselves looking at 4 300kcmil Al XHHW-2 wires in the service entrance mast, 2 per leg, along with 2 250kcmil wires for the neutrals since the line neutral lug on your meter base can't take anything larger. These give us a healthy 368A after the derate is applied, which is more than sufficient to meet our 332A requirement. (Were this not a residential service, you'd have to provide for the full 400A nominal requirement, which'd require another size bump to paralleled 350kcmil conductors.)

You are correct that 600kcmil is the right size for using a single wire per leg for the service entrance, though -- this gives you 340A at 75°C, just enough to meet our 332A requirement. Furthermore, it is about $0.50/ft cheaper at the time of this writing than the parallel conductors, and also takes up slightly less conduit area, albeit not enough to actually matter. However, the larger conductors can be more difficult to pull through the conduit, which may be an issue, although the reduced surface area compared to the paralleled conductors means you have less chance of skinning the wire, all the same.

Your numbers look correct 332 amps for a 400a service or 83% of the service is correct. I would verify that it is a true 400 amp not a 30/40 or 320a service both are normally called a 400a service. The meters I have connected to are only rated to 75c you may notice the utility comes in with much smaller wires this can be done for several reasons , first the utility is not governed by the NEC and second is those conductors are in air not in conduit as your service is required to be until the main breaker or service disconnect. I do not recommend parallel service drops on residential as I have seen a few problems where I have not seen the same with single not parallel lines problems both at the service crimp and the meter double lug one having a issue and 2 at the service crimp , this is very rare with many services but I have not seen the same issues with single feeds. 3” is normal but depends on the support and connection to the home.

Edited to add comments: Actually the grounded conductor is based on the size of the largest ungrounded conductor per table 250.102.c.1 grounded conductor... aluminum 500-900 requires 3/0 aluminum 1/0 copper. I think we all missed that and 500 is way overkill

Based on your concern on the AHJ: Well Oregon and Washington have a reciprocal license agreement because we use the same code and are even on the same version of the NEC, I could pay the fee with my license and be able to do it , no difference , not a problem You can always use larger wires, I provided the minimum based on your ungrounded conductor with the code reference if the AHJ were to question it. Harper was joking about #10 but was accurate no pro would waste that much wire and make the pull harder than needed.

You can use larger wire you asked and your ungrounded conductor’s were appropriate, but the grounded conductor was way larger than needed Many 240v loads don’t even have or require a neutral like your electric water heater. Some 240 loads do require a neutral but most can be down sized to 70%.

One 400 CU THHN per phase and 250 CU THHN for neutral is what the NEC allows...

Since this is where the utility connects you in, they make the call on what wire they want to see poking out of the masthead. It sounds like your utility is requiring doubled 350MCM Al, so 6 wires, two of which are white taped, pokeing out of the mast head. Your lucky, the Al will be a bit cheaper. I just did my own 400A upgrade, and TEP (Tucson Electric Power) required single lines at 600KCML Copper. This short 20' run is very expensive for the copper. They said they did not have the couplers for "doubled" lines. The funny part is, their connection from the pole to my massive 600 size copper wire was singled 250KCMIL Aluminum... they don't live under NEC code and have the advantage of "Air cooling" of the lines...