Cheap relative positioning

Current mobile phones with a multi-constellation GNSS chip might yield you submeter repeatable accuracy.

A Garmin GLO is about $110.00 but one foot positional accuracy would be difficult to obtain. This would be true of most consumer grade GNSS receivers at this time.

Handheld laser distance meters with a range of 330 feet can be found for around $100 to $200. (Bosch, Leica, and others)
You could use one to locate two or more permanent points (Fence Posts, Building Corners, Prominent Rocks, ETC.) on the property from the plant locations so long as the permanent points are visible from said location. This is the modern surveying equivalent of two-taping. The solutions will be better with strong geometry if only using two reference points. (The closer to a right triangle, the better.) Semi-permanent or permanent reflective laser targets could also placed as reference points. (You could also use bicycle reflectors, or reflective tape.)

You could go old school and define a grid with a transit and steel tape. Create three permanent points which form a right angle at locations which will not be disturbed, and encompass the area of interest. You could then measure the distance along each line to the plant locations. (Latitudes and Departures, or Up and Over measurements)

If you are patient, and have a helper or two, you could do the above without a transit by using two steel ( or cloth tapes) and squaring up the grid using Pythagorean theorem. (This is really old school)

The above suggestions are dependent upon terrain and vegetation, but are workable for a reasonable cost.

I have yet to see a radio translocation/triangulation solution which would provide the accuracy you desire, for a reasonable price.

Yes. I think you can get good relative locations of plants for cheap.

My suggestion to you would be to adopt the model I use to inventory trees. I use QGIS and QField to centralize my mapping and field data collection. QField can be used to digitize the location and collect information in the field and QGIS is where you store, organize and analyze the information about the plants. Both are free, and if you don't already have a compatible device, you can get a tablet that supports QField for under $300 (and I'm assuming you have a desktop for QGIS based on the fact that you posted this question).

For cheap, free software is unbeatable; sometimes good data is not free. Lucky for you is that it appears Columbus has orthophotography available through a WMTS, meaning you have free access to very current, high-resolution (3"/7.5cm) aerial imagery. It is more current and better quality than Google Maps. It has also been updated biennially since 2007, so you may in fact be able to locate your crop from last year in this year's imagery, and as it gets updated, you may be able to see your plants in subsequent years' images.

With current, very clear imagery, you should be able to get rather accurate relative locations for your plants (located in a global reference, but for no extra money). For obtaining high-accuracy locations, we have a GPS unit capable of delivering 4" (10cm) precision, but this unit cost thousands of dollars, and then there's the cost of real-time correction to get it to that precision. I don't think sub-foot accuracy that you can trust using GPS is going to be cheap, and to verify/improve its accuracy you'll probably want to bring the data into a GIS anyway. Digitizing with imagery uses a different relative measurement (so in this case, relative to landmarks identified by your eyes on the map and in the field), and is likely more accurate than relying on the GPS on your phone/tablet the great majority of the time. You could also support your locating by measuring distances in the field and in QField to establish control points, or locations of individual plants. If your device has an integrated GPS, QField can interact with that; it's better to use that to lead you to a location than collect the location outright, though.

Something to consider is that your time costs money, too, if you're doing this for a living. While high-precision equipment can cost a lot, it also can save you a lot of time. I think what the digitizing solution does is saves you money, but also saves you time in the field. So other solutions may cost little capital, they may end up costing way more in time. The other thing is that consuming and using that data should be easy, and with the abundance and cheapness of good GIS technology, collecting data in identical or closely compatible systems definitely helps that. You may be able to collect information with pencil and paper, but manipulating that data can be time-consuming and error-prone.