The suggestion of a trailer is the best one IMO. Good job Steve!
Eric- I very much agree with the weight comments. But this can be a do as I say, not as I did. (On my part cross country tour in 2017 my bike and load weighed in at 111 lbs in Missoula, at Adventure Cycling's offices). So I very well know this weight issue
bloom87- Hybrid? Really? That frame has a really short chain stay for a recreationally intended bike. Also the chainstay/seat tube angle is pretty open, suggesting a fairly high BB. What brand and model is it? I could be easily wrong but my eyes don't lead me to think my opinion is off. When you "miss label" a bike it's hard for us to assume different, especially when we see visual aspects supporting your term. I never made reference to the seat height. I did comment about it's far forward position on the post clamp. Was that confusing? if so I apologize for not being more descriptive. There are many wanna be CX bikes with eyelets and rack bosses out there. (Surley and Specialized come to mind). Having accessory options does not make a performance geometry work any better for the loads and use the mounts might allow.
I doubt that larger tires or a different wheel will make a significant difference. I have built myself 4 touring intended frames and the earlier three suffered from shimmy, even at low speeds. I have spent hundreds (more like thousands) of miles with the bike wiggling along at 12+ mph. The first three had in common classic road bike tubing diameters but varying geometries (and trails) as well as increasing tire/rim sizes. It is number 4 that solved this shimmy. The biggest difference is the OS tubing diameters, including the little mentioned influence of a stiffer steerer (now also larger). I am confident in what I say about touring loads and the bike's design. That is why I went to the external lateral suggestion right away. it offers the most increase of total frame (but not fork!) lateral stiffness for the least work or insult to the frame's existing construction.
But as I qualified my first reply I see this as a somewhat senseless project. get a trailer and be stable. Andy