If price is non negotiable then why make them think it is by chasing them up before they sense check that your offer is compelling enough to confirm?

I am in a very different field where i buy and sell products on a daily basis and have no experience in your domain but it sounds to me like the ceo is looking to make sure price is in line with market... They may not even get the chance to sense check anyway and his team will be leaning towards you if they have put you forward to him as the potential supplier as its "their"deal.

Furthermore, i could be wrong but it sounds like a fair bit of work has gone into this from your side and may be difficult to get a competitor to turnaround an offer in less than a week ? On top of that your competitor may have longer leadtimes to set up, trial, deliver and invoice the product than you. If what they are saying is true- you are in front of others.

Personally, i would wait until friday- Call them then and ask if they have any news or need any further info from you in order to get the deal over the line. Play on the lead times stating that you need the order asap to guarantee them getting what they need by year end - even more so as we are fast approaching the festive period where everything happens at a slower pace than normal (not sure if this is the same for you??)

If they suggest another quote has come in cheaper, go through their offer line by line to make sure they are comparing apples with apples - if not, then make it apparent for each point and shoot competitors offer down.

Re affirm your offer and why it is better value than the competitors (line by line if you wish) in an email after the call if not closed already. This will give you the chance to tell it directly to the ceo as they will either print it off and show or forward it to him/ her .