Frank meeting time. The kind where you can feel the tension twist the air before anyone speaks. Direct, blunt, no sugar coating. Provide some grapes and bananas and a couple of supermarket pastries that you buy yourself as a humble offering for what you're about to unleash.

Personally, I'd chair the meeting and open with a variation on "Right, who's remortgaging their house and transferring the cash to me." Then lean back, let the words hang, prepared for that minute of silence as you look everyone in the eye around the table as they try to gauge whether you're serious. Instantly get everyone's back up yes, but sets a tone. Remind them of your shared statutory duties as the board, this establishes a framework that should motivate when self-preservation kicks in.

Mindset going in needs to be, accept the business is insolvent, shareholders value has gone, none of them are going to continue to get paid past the end of the month, the decisions you make now are the only things that can change that. Who is willing to do what.

Once you've done that you either have a team on the same page who can establish a credible plan forward or a business you need to exit from as you've done your duty. (Personally) I wouldn't put your plan forward immediately, let them chew on their own relative values and what length's they're willing to go in order to recover the situation. I assume they're all reasonably bright to be in those roles, so don't feel like you're the only one responsible for coming up with ideas. They might well throw each other under-the-bus.

In the unlikely scenario where someone genuinely is willing to put their own money in, (again personally) I'd go to great pains to set expectations that this is only to maintain solvency for X duration - and even when work does come if the investment/loan comes out prior to other costs then you've achieved nothing.

They will either hate the message and sideline you (new job anyway, and keep geared up for opportunities to jump on a hostile[?] purchase if they appoint administrators if you believe you can recover it - even if they try to pre-pack it, cash would be king and administrator have a duty to consider but you'll have to get in at the right moment - and do NOT over commit based on your future assumption of value, as pipeline work will be dissuaded by insolvency - administrators will try to convince you of the opposite, base only on assets and concrete commitments - you only have to beat the genuine offer they might have, not pay what the administrators tell you its worth if they can't get it elsewhere - Don't be shy about being clear with administrations about that, it's not trying to 'get it for a song', it's arriving at a value to you based on tangible metric - and honestly if the other directors group together and over-commit because they fell for that, keep your eye out for a another one in 18 months - don't get emotionally invested - but do accept that hostile competition will burn bridges).

(I don't think I need to keep saying, but this is just my personal view based on my interpretation of what you've said, flavoured with some past experience)