Currently for tier farming, haybots will reign supreme. It's simply the only way to truly pump large numbers of fields up in influence. My suggestion to deal with this problem is a right click option that causes a farming action and turns the field fallow. Turning a field fallow forces the field to go through some form of growth timer, preventing planting on it until the field has been re-tilled. Fallow fields will neither donate to nor take away from influence bars. The benefit being the next crop to be planted will get an influence bonus based on the S/C value (rng based like the plenty bonus of course) of the planter + a base amount. The times and bonuses are obviously a balancing issue I'm not going to meddle with, but 300% is what I consider to be a minimum Influence value in order to rank up the tiers of a crop. This will not of course make haybots worthless, but it gives a semi-competitive option to players who choose not to use script aids to play the game.
Fields left fallow are often colonized by clovers, which are very good at replenishing depleted soil with nitrogen through their symbiotic bacteria. This opens up the possibility for an uncommon curio along the lines of a "Lucky Four Leafed Clover". This is also of course a traditional farming method that fits well with the period.