Can I negotiate an acceptance to print delay, post acceptance?
It's hard to tell from the outside why they aren't posting online versions of your accepted paper now. If the publisher is the root cause, you could conceivably change their mind by negotiation. I would not be hopeful because they're likely to keep to the status quo purely out of inertia, but your objection would probably be filed away as a data point for when they finally decide to modernize.

On the other hand if the editor-in-chief is the root cause, the publisher is not likely to overrule the editor-in-chief, and you'll have to convince the EiC. Chances are the EiC has entrenched views of this (as opposed to the publisher who's more likely to simply be doing what they've always been doing), which makes convincing him/her harder. Still, you could try. Be sure to mention you have follow-up work already lined up.

It's unlikely that there'll be negative consequences for trying and failing. Your paper's already accepted; they're not going to rescind it for non-academic reasons.

One thing I would definitely check is whether you are permitted to upload preprints. You mention there's an embargo, but quite often the embargo is only on the accepted manuscript. You can still post preprints. Some publishers (e.g. Elsevier) allow you to post the accepted manuscript as well, on a non-commercial personal homepage or blog.

Edit: based on that paragraph, negotiation is the only way out, because they're preventing you from making anything else publicly available. If you have transferred your copyright then they can actually publish without your consent now (still, they might let you withdraw anyway as a gesture of goodwill). You say you haven't signed any copyright transfer, but that's not sufficient; the journal might have policies that say the copyright is automatically transferred upon acceptance or even upon submission. You'll have to check. If you haven't transferred the copyright, then you could withdraw and submit elsewhere. It's a decision you'll have to make.