OP, I am very sorry to hear about your illness and you sound like a great dad. It must all be very painful.
You have asked for insight and I can maybe share a bit, because my ex also has advanced cancer. He has always been a very full on, decent dad. I have not limited my dd's contact with him in any way.
However, I do see reasonable arguments for not increasing contact. Firstly, your desire to do so feels (understandably) motivated by your need to pack in as much rich experience as possible with them - I would say more for your sake than for theirs. For them, I can imagine this being quite disorientating and overwhelming - not without pressure ("daddy's sick so we have to do all this stuff, have all these magic moments, and if I don't fully enjoy and be a wonderful kid for him during this time I am failing him").
Also, and sorry to be blunt, I think your ex has some point. Though sounds like she expressed it without much nuance. For the children, it is vital that they have a secure base that is there for the long term.... and also, is there with space relatively away from the stress of illness and hospital visits, while you are ill. Of course they must know what is happening, so they can emotionally adjust, but this is one advantage children of divorced parents have if a parent is seriously sick - that they have a parental base away from the site of stress and illness that will remain unaltered throughout. That does not mean that contact with the sick parent should be reduced, but to increase it to 'pack in good experiences' just to then withdraw it more painfully if things go bad does not feel like a process focussed on the child's wellbeing.
Neither is spending valuable time you have wrapped up in court, or putting your children through the stress of telling a court whether they want to spend more time with their sick daddy.
If at all possible, I would spend your time and energy working things out with your ex instead - in a way totally centred on your children's wellbeing. Read some books and guides on how to support children through parental illness and do it together.
I have sat with my ex and worked out and agreed the best way to talk about his illness so they can understand it and cope with anything that comes. I have made our schedules totally flexible so he can have them on days he is well, and I am with them in days when he is in the hospital/ not well. We both tell her any key events/ developments together. While he is unable to do active things, I have taken over doing those things, and don't watch fun movies etc with her, so he still has something to do with her that is special, despite his limitations....
But piling in extra time with him I don't think would be better for her. It is incredibly stressful having a sick parent, and time away from that is extremely important, as is encouraging the children to continue all their hobbies/ interests etc independent of their parents....
I hate to speak bluntly, but if you are to lose your life, then your ultimate objective in your remaining time is to help them be strong, resilient, and able to cope without you. It sounds like you already spend so much time with them they will be packed full of happy memories, regardless of whether you increase your contact. And they already have no doubt that they are loved deeply.
I hope this helps and am sorry if any of it is upsetting.