Hi, Maybe a photo of the lamp holder issues would help us.
" .. I doubt they'll fit on the table top and there isn't room for floor stands .. ". I see.
Then maybe your solution could be made to work.
Depending on the total weight of the light fixture .. You could start with a Superclamp on the table edge and attach eg Kupo's Max Arm. That offers a position flexible 5/8th in Stud for the light fitting. If you needed more height, add a solid 5/8th in Alu rod (vertically)(drops into the Hex socket nicely) topped with a Grip-head or radially grooved swivel adaptor (as shown) between the Superclamp and the Max Arm.
Here I have over complicated things to illustrate some of your options. There are alternatives available to use at A,B,C & D - you could, for instance, simply use another length of Alu 16 mm rod between B and D:
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