Do you understand the logistics of supplying such a force?
Trondheim is only 50,000 people.
Where are you going to position these troops around the fjords ?
Yes, insofar as a chap without military education/experience can, but with the background of 27+ years reading and study. Each division will need ~500 tons per day, an increased allowance cover the exigencies of cold weather operations. I wouldn't think that the field forces of the early war would approach the late war divisional slice requirement oft quoted of 700 tons due to the unsuitability of Norwegian terrain to the same extent of motorised operations postulated for France in 1944/45. There wouldn't be much change out of 20,000 tons per week for the ground forces.
On top of that, there would be a requirement for quite a few airfields, both forward ones for fighters around Trondheim and rearward ones for light bombers and strike aircraft as well as long range fighters at Namsos; I don't have any figures on the necessary supply needs (fuel, lubricants, ammunition, spare parts, bombs plus food and necessary personnel supplies) for 200 Hurricanes, 100 Spitfires and 100 Blenheims (or more preferably a proper dive bomber adapted from an RN development in the 1930s), but would be very interested to find out; they would be supported in turn by long range fighters and strike aircraft operating from Scotland and the Shetlands. I'd think it might be in the region of 250 tons a day, just as a wild guess. The weather will have an effect on the possible scope for operations, which in turn will impact the needed supplies.
I don't know the port capacities of Trondheim and Namsos during this period, but they would necessarily need to be increased to support such a force, including construction of a new dedicated port in Trondheimfjord and associated infrastructure. I'm further not sure on the food/supply production capacity of Northern Norway, but would presume the majority would be focused upon localised civilian needs rather than any considerable surplus. Again, I'd be quite interested to find out.
If the Kriegsmarine has been very nastily dealt with, then the possibility of being outflanked by German naval transport or amphibious assault is minimal. That leaves their possible lines of advance as coming up the Dovrebanen through Dombas or up the coastal road system. The former is more likely, given the importance of having a railway to support an offensive; a priority would be disabling the line up from Dombas if it fell to Jerry. Andalsnes is important as there is a railway line between it and Dombas since 1924, so at least one corps would be based there, with the other at Oppdal and a Norwegian division covering the flank to Roros.
The Germans would be operating aircraft out of Stavanger (555km away from Trondheim), Bergen (461km) and Oslo (391km). The Bf-109 in the early war is going to have a combat radius of 300km, which is going to put it out of the picture for operations other than from limited forward airfields. The Bf-110 can make it from Bergen and Oslo, with the former being a more limited base; the combat record of 110s up against single engine fighters isn't the best. That gives a window of potential for the establishment of land based air in the Trondheim area of operations, whilst covered by RN carriers.
The strategic advantage of holding half of Norway is that it allows for purchase of Swedish iron ore through Narvik, with a knock on effect on the broader British shipping situation and industrial production if and when French North African iron ore shifts in availability; allows for more general courting of Sweden, including buying ball bearing production or a portion thereof; allows for more effective Allied engagement with Finland from 1940 onwards, potentially preventing them jumping into the Nazi camp for Barbarossa and the Continuation War and fairly significantly impacting the Eastern Front, including preventing the same level of losses from any Arctic convoys; it saves hundreds of thousands of Norwegians from the tender mercies of German occupation; it severely constrains the Kriegsmarine from being able to contemplate surface operations out into the Norwegian Sea and breakout operations into the Atlantic; it deprives Germany of Norwegian heavy water by putting the Vemork plant in range of air raids that would make its ordinary operations quite unlikely; and ties down German land and air forces from other theatres, such as the Mediterranean.
The combination of those advantages make the eye watering logistical price worth paying.
Given that the RN can't reasonably interdict the invasion forces bound for Oslofjord and Stavanger apart from submarines, cutting off the whole Norwegian campaign at its initiation would seem to be rather difficult without extraordinary luck bordering on the supernatural. If a march can be stolen on the Germans and a window open up for holding
Southern Norway, then matters shift even further. I agree with your earlier conclusion that it would be a logistical headache to garrison and defend Norway, but the British Prime Minister in 1940 was the same chap who advocated the Greek campaign of 1941.