FYI, YOU will probably have to move any and all plants, even if you will have YOUR furniture moved by a professional company. They usually will NOT move live plants. It does sound as though you will be doing your own moving, but don't try to get a moving company to take even a few last-minute plants - they MIGHT since it seems this is a move within a state, but I doubt it. Renting a large truck might be the best way for you to make the move in the fewest necessary trips, especially considering the price of fuel now! I would take cuttings of whatever you can, even if they grow slowly, and especially of the things you value, for rarity, looks, etc.. If you can, dig up the most recently planted stuff that you REALLY want to take with you, pot them up into pots at least one size larger than the pot they came out of - to accomodate new root growth - you may have to do a little root and top pruning, which I don't like to suggest, but..., needs must. Keep them in a slightly shady area, dappled shade or early morning sun, and water, probably daily, but it's easier than digging hundreds of plants all at once. You may be able to beg or buy large pots from a local nursery. If not there, try a local landscaper. Since you will be building, DO NOT even try to put beds near the house - the construction crew(s) will trample them, drive over them, etc., etc.. Save the wear and tear on your nerves and voice, and your relationship with the crew(s), and plant in "nursery beds" well away from the construction. You can plant things (too) thickly there, and thin out and move closer to the house as construction is nearly done - by which I mean painted, gutters up, AC/heat pump, pathways in, etc.. This does mean that things will be multiply transplanted, but most of them will make it, and having them in the ground will be easier than having them in pots. You CAN build paths and put in other hardscape - fencing, arbors, pergolas, etc., as the house is being built, but plants just aren't "seen" and get walked on. Oh yeah, invest in 8-10 bales of straw, and lay in down heavily around the site, it will avoid a world of mud and mess being tracked into the house. You can rake up the residue and compost it when they are done and you are ready for making beds and planting. Save some of the chicken manure (or use a new supply if you have access) for putting on the beds closer in as the construction winds down. If the chicken manure isn't well aged (at a minimum, 6 months) then you can make a pile of it and borrow a tractor to turn it several times while the construction is ongoing - it's amazing how fast a pile will shrink as it breaks down, so make a bigger pile, or more piles, than you think you will need. If it is gong to be at least 4 months before you will be planting in a bed, then you can just mix it in and let it age on the spot. Another suggestion, from experience, is to run water lines out to the garden area as the house is plumbed/wired, as well as electrical lines for lights, fountains, etc. It's a LOT easier to run lines from the beginning than to run them later. I put hydrants on all 4 sides of my house, and 2 further out, and am glad I did, as it's much easier to run soaker hose systems from each spot, or to hook up a hose with a sprayer for new plantings that need more water. With a good well, and using y-connectors, I can water several areas of the garden at one time.

The above is not bad advice.........except: an established clematis that has a root system that can penetrate 4' (and that's not an exaggeration) into the ground will also have a root system much wider than the 12" recommended root ball. It is just as important to obtain as much of the horizontal spread as it is to dig deeply as the horizontal spread will contain much of the fine feeder roots which are essential for the vine's reestablishment and continued health. So picture if you can what a correctly dug established clematis vine could look like: a rootball at least 18-24" wide and 30-48" deep. That's a whole lot of soil and roots to attempt to move, especially if transporting any distance - like from one residence to another as opposed to two different locations in the same garden. Obviously, containerizing something of this size will be very difficult. A younger, less established vine will undoubtedly be easier to dig and with a smaller rootball, but you've got complications added with the competition of the tree roots, which will impede digging a clean rootball. I don't mean to dissuade you entirely from this process, but keep in mind it is not a guaranteed deal by any stretch of the imagination. If you do attempt to dig and transplant your vines, I'd be inclined to attempt to reproduce them by other means just as a form of added insurance, especially if you have the luxury of some time before the move must be made. I've included a link to a pretty fair overview of other methods of increasing your clems - you might want to give a couple of them a try. Layering is perhaps the easiest, but does require some time. Although most sources recommend doing this in late summer or early fall, I've found that the new growth produced earlier in the season will layer just as readily. Even though financially challenged with the expense of a new home or whatever, determined gardeners always seem to be able to find a way to obtain the plants they want :-)) You may not be able to afford to purchase all the clems you want immediately, but I bet you'll be able to squeeze out a few bucks here and there to add to your collection. It's amazing how fast foregoing a few lattes or the occasional opting for hamburger rather than steak will add up to a new plant for the garden. Remember the priorities!! Here is a link that might be useful: clematis propagation

If you don't see signs of blooms, or don't mind sacrificing the chance of it blooming this year (which doesn't sound likely), I say go for it. I never mind much about preferred transplanting times unless the plant is fussy (which then it wouldn't be growing in my gardens) or I really want to wait until after it's bloomed.

If it is already attached to the trellis in the container, it is best to leave it attached for now. Attempting to undo it and reattach to the new trellis will undoubtedly damage the very fragile stems. Next spring, after it is pruned back hard, you can remove the plastic container trellis and train it on the permanent one.