Danny - it's hard to judge the sense of things not being in the discussions, but for what it's worth, my perspective is that you may be approaching this from the wrong angle.
You say "Overall, they love our solution and want to move forward, yet they have asked us for a cheaper price". As Jimg notes, everyone is after a lower price, but that isn't a valid reason to give them one.
I would focus on the value you are bringing to their organisation. If there is no lower priced equivalent on the market, and if your product is going to bring them substantial value (i.e., through cost savings, higher profits, all-round easier lives, etc.), then they have two alternatives: pay what you are asking or go without. Given the strategic importance of this deal, you have to weigh up the likelihood that they'll take the latter course of action.
This doesn't mean you sit back waiting for the customer(s) to cave in. I believe you have to help them build their business case in their minds - demonstrate to them the money they will save/new sales they will bring in/etc. People want to feel that they are getting good value for money, and this isn't the same thing as getting a decent discount. (My sense here is 10% is peanuts to them, but less so to you, so by opening up the discount discussion you may make a rod for your own back - they may have 30% in mind, you're not prepared to go above 15% - you both end up having to walk away from the deal in order to save face.)
(NB Of course, if there are equivalent products out there, it helps if you have established a sound relationship with them - people would naturally rather buy from someone they trust and like than someone they don't.)
On a related point, I would also think twice about your approach to implementation and training services. I myself am guilty of giving away consulting effort, but I'm still in the first six months of my latest business and trying to establish my name. After two years, although I understand the point about customer development (same here), I think you should put some value on your implementation and training. If you give it away, customers perceive that it is a) low value and b) in never-ending supply. Unless you want to be in the consulting business, you should make it expensive for your customers to use too much of your time. You can by all means provide the customer with a certain amount of consulting in the price, but my point is that you should put a price on it and make it clear that there is a cost somewhere in the equation.
Coming back to your meeting in a couple of days, let me share with you the best piece of sales advice I was given as a young entrepreneur: "Shut up and Sell!".
Hope you get the deal!