You seem to be making it harder to test than is necessary. Assuming you're talking about a small electric hob designed to be plugged into a 13A socket on your kitchen ring main, just unplug/switch off the fridge for the required time to get a useful reading off the supplier's meter (or else use the plug in monitor).
The fridge will keep its cool for an hour or more provided you keep the door closed and it shouldn't take more than 10 or 15 minutes of rev/led blink counting on the meter to collect the data you're after (assuming you just want to verify the manufacturer's data on element wattage(s) - select maximum heat so the stats don't kick in too soon).
An electric oven is usually connected to a cooker point fed via a dedicated spur from the CU, usually 6 or 10mm FT&E cable fused at 45A (same applies for the immersion heater but fused at 15A using 2.5mm FT&E). You'd need to make sure everything else was shut off to test this by counting revs/blinks at the supplier's meter.
Again, you can set the oven stats to max to verify the manufacturer's wattage figures for the various heater element combinations. Any further analysis regarding real world consumption will be a matter of stopwatch timings for the on/off cycling of the thermostats during a typical cooking cycle and temperature setting. For heavy duty fixed wired loads, the use of a plug in energy monitor is precluded so you're really stuck with timed consumption registered by the electric meter or a whole house energy consumption meter. You'll have to shut off every other load in either case.
A clamp on whole house energy meter might have an option to measure such loads by allowing you compensate for the effect on the conductor and insulation thickness variations (possibly by using an optional plug adapter to pick up the voltage from a handy 13A socket such as the one commonly incorporated into most cooker points)
I'd expect the outer of the clamp to have an electric screen to isolate it from such external influences. I haven't seen the spec on any of these clamp on monitors but I could well imagine it might well cater for an accessory 13A plug and cable to get a more reliable access to the Live and neutral for sensing the voltage component. Such an accessory would be most useful to allow testing of other fixed wired kit where there's room to clamp onto the live wire to sense the current component.
If the transformer is a modern one with built in thermal fuse protection and mains terminals designed to accept 2.5mm FT&E cable, he's probably wired it into one the ring main circuits using a short length of 2.5mm FT&E.
I'm not sure whether the older designs of decades gone by were designed to be so directly connected to a 30A fused circuit. Possibly they required a mains connection via FC box with a 1 or 3 amp fuse fitted. I'd check that your existing one has been safely connected to the mains.
I tried searching for info on these little power vampires but the suppliers/manufacturers seem just as coy about the running costs as the manufacturers of UPSes are, i.e. no information whatsover on their efficiency or idle consumption. However, one interesting point that stood out was that the overheat protection was a one shot deal in that once the thermal overload protection had operated, you would have to toss it away and buy a new one. Fair enough in the case of a transformer fault but a kick in the goolies if it were simply due to an external wiring fault.
When we moved into the present house just over thirty years ago, I decided to make good use of parts I already had in my possession rather than spend money and make more work for myself, hence the ex-GPO trembler bell screwed onto the door frame behind the bell push with a couple of 8 cell AA battery holders stuck back to back with double sided adhesive tape to provide an everlasting 24v to lend the bell enough loudness (it could be adjusted to run off a DC voltage in the range of 10 to 24 volt - it wasn't really loud enough off just
12v, hence the 24v battery pack (now 27 volts).The alkaline cells lasted long enough, about 15 years or so. what retired them was corrosion which had damaged my home made 16 cell battery holder to the point where it seemed simpler to try a cheaper (and far less bulky) alternative. Despite all the corrosion, the bell still worked, albeit just a little bit queter than it once did.
Since the idea of using a large enough battery to, in theory, last for decades was rather flawed by age induced corrosion, it finally dawned on me that a cheaper, shorter lived battery option would be much better. Since the local pound shops were selling zinc carbon PP3's in packs of three, it was a no brainer to turn the whole pack into a 27 volt battery instantly ready to hang off the screw head I'd originally used to hang the first 'monster battery pack' off of.
All I had to do was solder a couple of straps and connect the resulting 27 volt battery to the bell wiring. The result was a less intrusive neater looking bell and battery installation which had only used a couple of feet of bell wire from the bell push which also activates the wireless bell push sender unit fitted on the inside of the door frame so the wireless door chime in my upstairs office could act as a repeater.
I added a a zenner dropper and reverse polarity protection diode so I could power the sender from the 27v bell battery but I kept the 12v internal battery which allows independent operation of the remote office door chime for testing purposes.
However, it has also proved handy for when the XYL gets in late from her nannying job to alert me of her return without having to shout to be heard through the closed office door against the sound of a TV program I would often be in the middle of watching at that time of the evening.
The battery powered door bell has served me well these past three decades with a running cost on a par with a mains powered bell but without the faff of running yards of bellwire and the capital investment of a bell transformer.
In this case, battery power trumps mains power despite the energy cost using primary cells being several thousands of times greater than what the electricity supplier charges. And, one more thing, it'll still function during a power outage. :-)
You're welcome. Sorry I couldn't offer any experience based help in regard of the bell transformer.