Given the conditions that you have described there is no good explanation for what has happened except that the fuses are faulty.
This indicates either that the fuses are faulty :-) - or that there is something incorrect in your described conditions. When things like this happen it is a good idea to ask "what really happened compared to what I think happened?". Sometimes human error creeps in very subtly and Murphy loves to confuse us.
All things being equal I'd guess you have some mislabelled resistors, or wrong low value resistors in a batch of apparently high value ones. See below.
The 200 mA fuses are probably NOT a safety issue but a meter protection one. Chances are the circuit may be damaged if a much larger amperage fuse is used. You could sacrifice one meter to see. May not be a good choice.
One way to try to bypass your problems is to place a say 125 ohm resistor in series with the supplies at a point that the students cannot access. Then max possible current is 25V/125r = 200 mA. A 100r resistor would not blow a 200 mA fuse. Fuses are typically rated to blow at 2+ x rated current. If an external voltmeter is used downstream of the resistor then the drop in the resistor is unimportant. If you are using a meter in the psu it may matter. If these psus are used only in this experiment (unlikely) an internal resistor could be fitted upstream of the meter. Not advised.
Another alternative is to set the supplies to current limit at 200 mA if that feature is available.
You could add series constant current limiter but that takes time and money and may not be desirable. An LM317 plus a 5.6 ohm resistor will make a 223 mA current limiter. It requires soldering one resistor to a TO220 part and 2 external wires. Wrap the whole unit in tape or heatshrink and put in series with psu +ve lead. IFt will drop 2 to 3 volts in normal operation.
Fuses: Inspect the blown fuses and unblown fuses CLOSELY. Are they all identical? Or at least, is there a mix of fuses that is essentially the same in blown and unblown batches. A clear physical variation points to a fuse rating issue.
Examine the fuse rating labelling with a magnifying glass. Are they 315 mA fuses or 31 mA fuses? 30 mA range would be very rare but do exist. Fuses will typically blow at about double rating but wide variation is possible so would be marginal in your application. Seems unlikely but ...
If you decide to bridge your fuses use the thinnest wire you can find and solder it across the blown fuses. You are unlikely to find wire that will fuse under 100's of mA. If you blow that then 'summat aglae'.
You could buy and fit "somewhat larger" fuses. Knowing what happens to your meters at larger currents may be good.
Some meters have very nasty internal resistances and so drop significant voltage. I measure and label cheap multimeters current range resistances to avoid being caught out. IF your meter has more than 3 ohms resistance on the 200 mA range it will drop > V = I.R = 0.2 x 3 =- > 0.6V. So a silicon diode across the meter will protect it from over current. A Schottky diode will protect against lower voltages. 2 x super cheap 1N4148 diodes back to back across the meter terminals may suffice.
Take an unblown fuse, place a small current (20 mA?) through it and measure the voltage drop across it. Note drop and slowly increase current. What is the voltage drop and current when it blows? Try this with a 300 mA fuse from other sources.
Measure the resistances of ALL the resistors that students used. Are the 2k resistors ALL REALLY 2k. Are there some 200 ohm ones in there. Or 20 ohms. Or 2 ohms ? :-). Note that it may not be the lowest intended value that is faulty. A 100k that's a 100R will fool you if you are lookng for a 2k/20r. Measure them all. Quickish way is to set psu high, put a meter on a eg 10 amp range then short psu through resistor and meter. If a 2k is 2k meter will hardly budge. If you get 200 mA+ you should notice it. Meter will not be hurt at 10 amps.
So - overall a mystery. Fuses are bad or something is not as it seems. Hopefully the above will provide some leads.