I'd go a step further and say that not only is a 4 season tent not necessary, it is a poor choice for most bike touring. You would be adding a good bit of weight, bulk, and expense for no real gain.
Where the wind is bad I do usually pitch the tent where there is a least a little shelter from the wind. It doesn't have to be much, a slight rise in the ground, a retaining wall, a berm, some trees, or even the edge of a corn field will suffice. It has worked for me even the wide open and windy country like Wyoming, Montana, Kansas, Eastern Colorado, and Texas. On the Trans America our group of three managed with a cheap 4 person dome tent.
If your tent has those little ties that attach the fly to the pole, you know, the ones we all ignore... Tie them if wind is expected, they make a big difference. Extra tie outs are another option, but I have never bothered with them and been fine in some pretty severe conditions.
I personally really like the Eureka Spitfire 1 for those trips where I use a tent. It stands up to pretty strong winds and is light and inexpensive (you can find them for a little over $100). It has enough room that I have been comfortable with my 55 pound dog in the tent with me. I prefer it over tents that cost 2, 3 or 4 times as much.
Then there is the fact that our level of exposure to suffering in the event of an unlikely failure is low when touring. So even if we had a tent failure, we would have a single miserable night, and find another tent or a place to stay indoors the next day or so.
I have gotten away from using my tent for most trips and take a bivy a lot of the time, but when I do take a tent it is my Spitfire. To me the one drawback to the spitfire is that the poles break down into a rather long package. Some folks find it on the small side and tall people might find it too short. The length thing depends on whether you are willing to have your head and feet in the tapered ends. The tent is actually very long. In any case I think the OP mentioned being on the short side so it should be a none issue.