When should I start negotiating?

Now. Negotiate now.

Line up as many dealers as you can / are willing to, and let them know exactly what you're doing: shopping for a delivery dealer.

Don't be bashful that you are looking for the best discount under MSRP, no extras, all fees included. Let them know you're looking outside of your area and are willing to drive. It will take a little bit of effort, and you'll want to get email addresses so that everything is in writing, but it works. Once you get some offers don't stop there. Tell dealer A that dealer X is offering this, can they beat it.

I've done this (not with the ID.4, but with orders and on-the-lot cars), and it works. Some dealers will probably outright reject you but others will deal. And even the ones that don't want to play, get a text conversation going with a sales guy because when they catch on you're a serious buyer, they may change their tune.

Reporting back - I called several local dealerships with a similar pitch - "Tell me how you plan on persuading me to make you my delivery dealer". Responses were universally unimpressive; no one I spoke with offered anything specific regarding pricing, fees, etc. I can understand not being able to speak to financing, given how long I've got before delivery, but no one seemed to be willing to make an effort to get my business. No one offered to reduce the doc fee, or MSRP, or anything else.

The only thing that was mentioned, but I'm really unclear on: I'm in Washington State, that currently has a sales tax credit for EVs worth about $2K - but it only applies to cars that sell under $45K. Given my MSRP (Pro S w/ Gradient) is almost $50K, I would not be eligible, but one dealer mentioned that this could be worked around in combination with a trade-in. He didn't offer details, but I'd guess the workaround would involve discounting the car and my trade-in by the same amount, so they make their money back when they sell the traded-in vehicle.

After that call, I began asking other dealers about that possibility, and was told that doing so would violate the law. But reading the text of the rule, it's not clear how (it says you can't subtract the value of a trade-in for the final price, but nothing about changing the sales price directly). Another dealer said they would consider reducing the sale price to meet, but only if I purchased other packages to make up the difference (effectively capturing the rebate, it would seem).

I'll try again in a month and see if anything changes.

There's a thread on the top of the Washington state sales tax exemption that's worth reading: Tip: Washington State Sales Tax Exemption

In my opinion the most difficult thing about getting the ball rolling with this type of negotiation rolling is collecting email addresses of the fleet or internet sales managers of the respective dealerships you're considering. Just cold-calling doesn't get any results -- it puts you on your back foot because they're taking "soft" calls all day and aren't going to commit to squat, their job is to get you in the door.

Even with the emails, a bunch are going to not respond, or just spam you boilerplate sales pitches, and you'll have to decide if those are worth pursuing to get a response or just sending to the delete bin. Of those that respond, you'll find some who outright state "we don't discount below MSRP" and others who are eager for your business.

I believe the key is to present yourself as assertive and a "now" buyer, "Next Tuesday I will be submitting my online order for... " and "...I am reaching out to X VW dealers in the state..." and "I will select the delivery dealership offering me the best price below MSRP, including doc fees / no add-ons..." When I did this with Ford, I used "invoice" instead of "MSRP" because that's a norm for American cars. When I did this with Volvo, since I was making the pitch to dealers with the options I wanted already on the lot, I stuck with MSRP. I think MSRP is fine for the VW deal because there aren't a ton of options.

Anyhow, if you've got the time, try it, check back, I'm curious!