I have done it a few ways now... Not sure yet which I like best.
I have done the daily work with a new foal. I still have that gelding, he is sweet, and you can do pretty much anything to him... But he isn't the most senstive horse in the world when it comes to cues. He's a bit more relaxed about any cue he's given and sort of has a "I'm getting to it, don't get yourself worked up" attitude. That may be his breeding. He makes an excellent beginner horse because he rarely over reacts to anything and always gives you time to "change your mind" (so if a rider pulls a bit too hard on one rein because they came off balance, he doesn't immediately follow the pressure, he waits a few seconds to determine whether it was "meant" to be a cue or if he should just carry on)
I did one where I left them alone, totally, until weaning. This left a bit of a job at weaning time, but the end result was a horse with no "personal space" issues at all. He was just plain more respectful, and a lot lighter to work with. Quiet, but, he could still tend to react warily to something new. He was herd raised with mares and geldings.
And then I did one down the middle of the two methods. I didn't push myself on him, but didn't not handle him either. He is 9months old now, so a long way from "done". Generally I find he is bold and curious, but still a bit shy about things like having me right up close doing "stuff" to him. He does seem to be a bit more in my face than my untouched weanling, but less difficult to send away than the handled foal. I let his mother and other mares and later some geldings give him his early education for the most part, but not without my influence.
At the end of the day, I hesitate to say what the best method is... And I think it really depends on your situation. You said you need to do a long trip with this foal, and I agree with you, I'd want the foal to be as comfortable around people as possible for that situation - just make good and sure you are training habits you will still appreciate when he is full grown. It really seems what they learn from a young age is what really sticks with them. Don't work until the foal's brain shuts down, make sure he is still as alert and "with you" from beginning to end... For some wee babies this is only a few minutes at a time.