North America just north of that sharp right turn North America makes on the Atlantic coast.
I didn't see anyone mention it, but I have a Tamron 28-200 that I don't even know why I still have a rear cap for because it is always on a body! This is my "I'm not sure what I will need, but I know this will do it" and traveling light lens.
No, it is not Nikor perfection, but it's about as close as you are going to get with this zoom range. They make it in all the major brand flavors you mentioned looking at above and it shoots Manual, AF, and digital with ease. A great all around lens and you can score one on ebay for under $100 because everyone is going after the Nikor with VR and silent wave while this lens is being ignored. Oh and as an added plus, it's a macro lens as well. It isn't excellent at anything but being a single lens, but it does do everything else quite well.
"Would you like it if someone that painted in oils told you that you were not making portraits because you were using a camera?"
"Shouldn't it be more about the joy of producing and viewing the photo than what you paid for the camera?"
What will be the purpose of 35mm gear in your photography in the future? That's the question you should answer for yourself before considering equipment choices.
The main weight/bulk problem in your kit lies not in the F5 body, but in the three lenses you mention. If you can replace the 80-200 and 300 with one or two lenses (e.g. 85 or 50+105) for your photography, then the resulting kit will already be much smaller and lighter, but still offer the main advantages of an F5-based kit. This is what I do when I want to go light, but still have the F5 as a body (i.e. 20-35, 50/1.4 and 105/2.8 or 180/2.8).
Otherwise, if you want to go really small/lightweight, IMHO there's no way around a 35mm RF, I'd recommend an M Leica and 2-3 lenses. Prerequisite would be that you can get by with having lenses only in the 20-90mm range, where that kind of kit excels. Incidentally, an M3 plus 2-3 lenses is my choice when I want to go really lightweight (the resulting kit weight is about the same as an F5 body alone, and the "bulk" is not worth mentioning).
I'm certainly going to be getting rid of my 80-200 2.8. Need to get a repair done on it first though, but it will definitely be going. I don't even want to think of getting a Leica, well not until I'm a bit wealthier I think!
You could pick up a F100 and start adding some prime lenses or if you want a zoom the 28-105mm is quite nice and pretty small. My light set up is the N80 and a 24mm and/or a 50mm. Probably not much out there lighter then the N80 with a 50mm f1.8. Nobody goes "Wow" when they see your N80. A couple of times folks ask me where the LCD is but that is pretty normal these days.