You could get away with a narrow bed, say 1 foot, wide no problem at all; however, as you say it would probably be beneficial to make it at least a few feet or a metre so smaller crops can be planted in the front such as lettuce etc.
Also, consider other climbing crops such as sweet potato where a wider bed would be better growing the tubers with the vine trained up the trellis - it's a very effective way to grow them.
Have you considered making your own corrugated beds?
Yes, years ago I did trial several DIY corrugated beds - I actually made mine out of poly roofing sheeting and it worked pretty well but the post structure I initially made wasn't long lasting and I was faced with the decision to replace all the hardwood posts or ditch the beds altogether and I chose the later. This idea came about at a time when galvanised/colorbond raised beds were hardly heard of... then once these hit the market it was easier (and probably cheaper) to just buy the ready designed raised beds and assemble them rather than build them from scratch so that's why I went down the raised beds kit path.
Here's a shot down memory lane of one of my first garden bed designs

You can see the newer raised beds (colorbond) in the background.
Below is a similar DIY raised bed using poly sheeting and poly irrigation hose with bird netting to stop possums. I used star pickets and hardwood posts as the framework. The poly sheets never deteriorated and overall the it was a pretty cheap way to make a raised bed with high sides but it looked cheap too...
I suppose with more cost galvanised corrugated iron could be used with H4 posts to build a really sturdy DIY raised garden bed; although, one would have to weigh the cost against buying the ready made kit beds and my guess would be overall the kit beds would probably be the cheaper and better option - but I might be wrong...