I think it WOULD be a good idea to get a couple more and separate the tomatoes and cucumbers out. As rainbowgardener mentioned, You may have been a bit over optimistic about the number of plants.
Here is the instruction PDF for City Pickers: https://www.homedepot.com/catalog/pdfIma ... 18c4cb.pdf
-- it says 2-3 tomato plants so....
When combining plants, be sure to consider their nutrient and sun requirements. Tomatoes and peppers need similar nutrient balance. Herbs need more nitrogen, but so do cucumbers. Also consider how and how much they would grow and what would shade the others. But you do need to stick to recommended number of plants for best results.
Dolomitic lime should be available from most independent garden store sources as well as the big box stores. Ace Hardware would carry them too.
Good luck! I'm experimenting with some second hand DIY planters that work on the same SIP (sub irrigated planter) principle this year. Since it's going to be raining again today for the third day, I think I will concentrate on planting the containers today....
Note that some herbs prefer and have better aroma and flavor if grown a little dry. These types of herbs probably won't do as well with force fed/constant moisture of these planters, and in fact they won't need them. (Mint should be fine moisture wise, but they are perennials and will try to take over the planter -- I suspect by the end of the season, you would find stolons -- underground runners -- snaking around under the plastic cover/mulch and trying to grow out of other plants' holes....)