My bed has a metal frame and the mattress sits on a number of laths of about one centimetre in thickness, spaced about ten centimetres apart. These laths sit across the frame and are supported by a metal strip which runs the length of the frame. To this metal strip is attached three square-section metal tubes of about three centimetres in thickness (one at either end and one centrally), and which rest on the floor. The bed is immensely strong and doesn't creak under any circumstances.
I assume your bed-frame is designed in a similar fashion, albeit of wood. It could be that these laths are not of sufficient thickness, including also the supporting upright struts. If it's not possible to secure these parts such that they support the weight without creaking, it may be worthwhile considering the purchase of stronger wooden pieces. It need not be too difficult to do this without the need of employing a carpenter. It may be helpful to ensure the floor is not uneven in this area, because these support posts should rest on the floor and support the flexing induced in the laths by the weight placed upon them.
I'm a bit surprised your supplier has not recognised these support members are critical to the continued use of the bed.