I sowed seeds for Causasian Spinach three years ago and now have two plants flowering at about 2 meters high (south Sweden), alongside my compost bin. We have a different zone numbering system so that doesn't translate as easily. However, Daron, I am a native Oregonian and know your climate well. It is close to the same here in this region, though some winters may be colder here dipping down to about 2°-3° F for a few days, but have only experienced that once in the 20 years I've been here.
In regards to more info from my personal observations thus far in growing the Causasian Spinach; I agree it could be a good perennial inclusian into the forest garden setting for an additional supply of greens and one that also fits into the climbing vine classification. I have only eaten it on two occasions... and a third tonight as I will be baking some spanakopita this evening using it along with New Zealand spinach as replacements for regular spinach. The taste to me is nothing special, just a green (no chlorophyll aftertaste, that's always good). However having grown and used New Zealand spinach in my food forest for the past six years, I prefer it to the Caucasian spinach, in taste and productivity, but encourage planting both for diversity's sake plus extra security with diverse edibles.
New Zealand spinach Tetragonia tetragonoides
in my opinion has both a better flavor, and is more productive. The leaves are much thicker than the Causasian spinach leaves, being nearly a succulent type of leaf whereas the Caucasian leaves are quite thin so in cooking requires much more for the same amount of volume. Leaf for leaf, the NZ spinach is about four times heavier (more water, no doubt). Wikipedia states that some places have classified the NZ spinach as an invasive plant. I can attest to that as being a possibility and I exploit that potential to keep it in my growing area. It produces one flower (one large seed) at every leaf node and is a sprawling grower quickly growing in all directions. It is a perrenial in its native habitat but here in Sweden it is only an annual, yet reseeds itself quite easily sprouting every Spring on its own, from the masses of previous year's seeds. In the gardening area where I keep it contained, to a degree, it starts growing from sprouts about the first of June, and unlike 'real' spinach it doesn't bolt with hotter days ... I guess with one seed at every leaf node one could say it is in a constant bolt, though. Whilst I am putting out and maintaining my regular annual garden veggies I note if and where the new plants are sprouting. If they are too close to an area that I feel they would overcrowd, I just pluck up the seedling. If there is ample space, I allow it to grow until it begins impinging on other favored plants at which time I either harvest the leaves for the freezer or add the plant to the compost pile as it makes abundant green biomass. It doesn't seem to continue growing from remaining bits of roots left in the soil. Additionally, the hens love it, so at times I have blocked off an area of the garden and invited them in for a week to scratch around and consume the greens. All in all, I don't feel that NZ spinach is cumbersome with maintenance work and tends to have a high yield of use in our permaculture system.
That being said, I would have to add that the Caucasian spinach might involve as much maintenance time overall; requiring more time in picking the same equivalent of food product, an annual removal of vines to compost, and as it tends to have masses of flowers/seeds that could be dispersed on the ground if they are of high viability then pulling up plants in unwanted places becomes the equivalent of weeding for the NZ spinach sprouts. I haven't noticed any great viability of the vine's seeds to date, though I have clipped off the flowers towards the end of the flowering stage. Nectar for little critters, up to that point!
Every year I allow a number of plants; Lettuce, Asian celery, Red Orache, Carrots, Fennel, Chard, Arugula, NZ spinach and a few others to seed and I allow them to remain in the garden through the Winter... self-sowing. After seven years of doing this we have a diverse food forest including many regular annual vegetables that are allowed to grow where they found a niche. Looking for food now is always rewarding. Our asparagus seeds being eaten by birds have now been transported alongside the road near the house and possibly elsewhere unbeknownst to us... just as they have brought to us numerous other plants such as the seven elder trees that we now maintain for wine and kombucha making along with pies, marmalade and syrups.
We still do germinate and sow some annual veggies, plus potatoes and squashes and tomatoes, but we have many, many volunteer plants that gives us a wonderful abundance. Sometimes if asked by my wife if we have any coriander, I'll respond...'yes, I saw some yesterday in 'aisle 3- between the yellow onions and the black mulberry' or wherever else I may have noticed a plant growing. It's just a new way of 'shopping' ....
Wish you the best....