Realistically your chances are poor and it seems such a wonderful idea,
I too had the same goals a long time ago when I first started flying.
The problem is of course largely the weather. Holidays for most at least are based on going on a certain day and coming back on another - if you are lucky maybe the window might extend over an extra day or two. The issue is the chances of being able to do this flight in VMC on two given days in the winter are very poor. There is a chance but it is not a good one. Worse, there is also a possibility that if you were really unlucky a sequence of three or four days when VFR is not possible is on the cards.
With an instrument rating the flight is more likely but even then I wouldn't bet on two given days both proving possible.
With an instrument rating and a deiced aircraft you are close to being in business and have better than an 75% chance of operating to schedule but then only if you are really current and flying airways regularly with an aircraft capable of at least oxygen FLs and of course with oxygen.
Other issues are inevitably weight. As you probably know you need a pretty capable aircraft to do that trip with anymore than two adults, the amount of luggage you will want to take and fuel.
In short it is such a lovely idea but without the right aircraft and qualifications and / or lots of time to spare it is very unlikely you will be lucky enough to run to schedule.
and even then ask yourself if you really want the pressure?