RoseParade,
A couple of suggestions. The big one is to put the ball in their court. Make the point that you would like to hear FROM THEM any suggestions for a role other than a full time field sales role that would work. If they es full time attention in order to maintcan't come up with a single example, it strengthens your argument that their minds were closed to the idea. If they come up with ideas (e.g. part time, but with some working hours every day of the week), you know what you're working with. The key in all of this is to sound dead helpful, whilst backing them into a corner. If you can throw in lots of questions ("would it be different if it was four days?" "would it be different if I also X, Y and Z) it makes it difficult.
One little recognised part of flexible working requests is that they do not have to offer alternatives other than what you've asked for (e.g. if you ask for three days, they don't have to offer four, even if they would accept it). You have to actively make their life difficult on that point.
They said "this role is pivotal to this strategy, and requires full time attention to maintain awareness of the customer demand." Confirm your commitment to maintaining awareness. Ask what developments they think would develop on the days in which you are not in the office so that you could think about ways to overcome it. Ask if there are agreed steps that you could take on your days off to maintain awareness if things are really so fast paced that it would cause trouble (e.g. do you need to check your emails first thing and at US start of business) Suggestions like that show how determined you are to maintain customer standards and take the wind out of their sales a bit.
Oh, and ask them WHY everything they say. Frame this as wanting to proactively address their issues and think outside the box to resolve them (puke at business jargon discretely). Sounds dead helpful. Makes their life a nightmare. Like WHY they believe that having a window when you are not selling would result in competitors getting the business. Surely (unless your business is particularly niche and time critical) if you lose business it is not because you can't do meetings on a Monday? Are there underlying issues about customer loyalty and satisfaction that should be resolved as a separate process?
Finally, I personally would throw in the fact that you have heard that the US manager does not agree with part time work. I would frame it as "I have heard rumours that X does not want part timers on his team. I really hope that that is not true and I think that I can be the person to prove to him that I can make it work. If you would like me to talk to X about his concerns directly, I would be really happy to do so." If they are doing this because X told them too, they will s* themselves at that. Also, if you do need to take action later, you've teed up your case. obviously, personal choice whether you go down that route though.