Papers I've seen using this method show it's possible to calculate the fraction of denatured protein by analyzing displacement in peak emission wavelength.
Have you tried doing that with your data? What do you get if you plot peak emission wavelength as a function of denaturing agent concentration? If these look like sigmoidal curves (you might need a log scale on the X axis) with a clear upper plateau, then you can apply the method mentioned by these papers because the signal you observe is correlated to the fraction of denatured protein and saturates (this part is important: the signal must saturate past a certain concentration of denaturing agent, because all protein molecules are fully denatured and therefore adding more denaturing agent won't give further signal change; if your signal doesn't saturate, something is wrong).
However, they use monomeric proteins with few Trp, whereas I have a dimer with several Trp
Oligomeric state and number of Trp residues should not matter, because peak emission wavelength is only correlated to the fraction of denatured protein. Total intensity will increase with more Trp residues, but you're not using intensity as a measure of the fraction of denatured protein (and if anything, it's good to have more intensity to begin with given the quenching effect you observe with increasing denaturing agent concentration).
plus some additional variability introduced by the different ligands.
To take care of this concern, you need two controls that:
1. prove that none of the ligands alters the fluorescence of your protein,
2. 979
prove that none of the ligands emits fluorescence between 300 and 450 nm, or if they do then you need to measure it to be able to subtract it from your total spectra, in order to recover the protein contribution to the total fluorescence.
For 1, record fluorescence emission spectra of the protein without denaturing agent but as a function of ligand concentration (span a few orders of magnitude) and see if the peak emission wavelength changes with ligand binding (it might change, which means the same assay can yield binding curves and Kd values for your ligands, which could also be useful!). Full ligand titration curves would be the most robust control, but you can simply use the same ligand concentrations as used in the denaturation experiments.
For 2, the simplest case would be that your ligands are not fluorescent, but you cannot simply assume that. Therefore, an important control you also need is to record emission spectra for each of your ligands at the concentrations used in the denaturation experiments, and this at each concentration of denaturing agent (or simply at 0 and max concentration: if there's no difference between these two spectra, you don't need to record one at every concentration in between). If the ligands emit fluorescence between 300 and 450 nm, you need to subtract that from your total spectra to recover the fluorescence arising from the protein only. 979