Electronic – Does a clamping current specification under Absolute Maximum Ratings imply that less current is OK

I think you've got it mixed up. The body diode is a part of the structure of the MOSFET and does not help when switching an inductive load with a single MOSFET.

The zener in the symbol represents the avalanche rating of the MOSFET and is of use when switching an unclamped inductive load. You won't see it conduct unless you exceed the voltage rating \$V_{DS}\$ and get to \$V_{(BR)DSS}\$.

If you are actually getting +/-12V out of the pulse transformer, I don't see any obvious reason why that part would not work. Your negative swing out of the pulse transformer does have to be sufficiently large to turn the control MOSFET on, when loaded with both gate charges (-10V would be good).

So my guess is that only 0.3 amps will flow, but when will the bypass diode in the PV junction box carry current? Where are tipping points?

The situation is far worse than you imagine.
The maximum available current from a series string of cells is the current available from the lowest current cell. A lightly shaded cell will reduce panel output. A heavily shaded cell will almost stop panel output - and as this happens reverse potential from all the unshaded cells develops across the shaded cell so that it contributes nothing. If bypass diodes are fitted current then flows in an appropriate diode around the shaded cell, and also nearby cells if the diode spans several cells.
Accordingly, panels and cells within a panel which are connected in series need to be matched as closely as possible both in performance and in received isolation (light) levels. A 1000 W/m² : 200 W/m² imbalance such as you suggest can be fatally bad and should be avoided by design to the maximum extent possible. Bypass diodes should be fitted to prevent large reverse voltages occurring across shaded cells as this can destroy whole installations, or worse.

Bypass diodes are connected in reverse polarity to a cell's output when it is acting as a current source. If the cell current is lower than the string current the voltage acting to drive current through the cell causes it to produce less output and then to reverse bias it completely. A bypass diode across the cell conducts when the cells reverse polarity exceeds the forward polarity of the diode. So none of a partially shaded cells output contributes to string current when the bypass diode is conducting and instead the diode reduces output by a diode drop, plus whatever voltage the shaded cell(s) no longer produce.

While this description may seem contrary to what you expect, you will find it well described in many online articles.

Many examples can be found here and here

The effect can be easily visualised using the diagram below. For the diode to conduct the usually -ve terminal of the PCV-cell must be positive relative to it's usual +ve output. No current is produced.

Diagram from Dale Marshall here

Note that in the absence of bypass diodes the full remaining string voltage will build up across the shaded PV-cell. In high voltage systems this may be in the 400-1000 V range. Cells with defects my have low isolation voltages and break down. In such cases fires can (& do) occur which destroy the cell concerned, often damage others, will usually write that panel off and may destroy the whole installation or even an the building it is mounted on.