Conformation change sometimes changes tryptophan emission maxima, if your ligand is not fluorescent, you may try a simple experiment, first excite native protein at 295 nm and measure the emission maxima and then add saturated amount of ligand to the same concentration protein and measure the trp fluorescence again and monitor any change in emission maxima wavelength.

Similarly you may try CD experiments to detect changes in secondary or tertiary structure provided your ligand is not optically active.

However, fluorescence is more sensitive and easy to check.

Despite the technique you use for detecting conformational changes (CD or fluorescence), another way to understand if you have conformational changes which cause increase in reactivity (positive cooperativity) is to study single protein conformation. To isolate single protein conformation you can use crystallization, followed by enzymatic assay on microcrystals suspension or single crystal microspectrophotometry. Otherwise, to overcome the problem of crystallization, the enzyme can be encapsulated in silica gel, a matrix that prevents or slows down conformational transitions. Being a transparent matrix, all spectroscopic studies can be done on the encapsulated enzyme as in solution. If your encapsulated enzyme behaves non-cooperatively, you can confirm that a conformational transition causes a cooperative behaviour.

As the other respondents have said, CD or protein fluorescence might give you independent evidence of a ligand-induced conformational change, but the most compelling evidence comes from the method you have already used, the activity of the enzyme, and a Hill coefficient of 2.4 leaves little doubt.

Turning to the second half of your question, the process of allostery depends on an equilibrium between the two conformational states which is influenced by the substrate ligand. However, if some other substance is also able to influence that equilibrium and effectively lock the protein in one conformation, then you will get MM kinetics.

if you encapsulate your enzyme you should have the effect of blocking a single conformation as Paul suggested to be done with a substance (an allosteric effector). For example, if you encapsulate your enzyme in a solution without any substrate, you block the conformation with low reactivity. Then, if you add your substrate you should see MM kinetics corresponding to the low reactivity state

Cooperativity can be caused by backbone motion within a physically linked pathway through which the change is propagated between the binding sites and also by conformational changes in side chains only, but can also be caused solely by changes only in the frequencies and amplitudes of dynamical fluctuations of the protein.  For example, transferred changes in protein motion alone, cause the catabolite activator protein (CAP) to exhibit cooperativity with respect to cAMP; the binding of the first cAMP molecule has no effect on the conformation of the second cAMP binding site yet the second molecule binds with less affinity (negative cooperativity, Hill coefficient < 1). The dynamics of the protein are, however, affected; binding of the first molecule of cAMP augments motion whereas binding of the second cAMP has the opposite effect.  This dampening of protein motion is entropically unfavourable and causes the observed drop in affinity for the second cAMP (see Popovych et al, 2006 DOI 10.1038/nsmb1132   for the methods used).

Also, you could use isothermal titration calorimetry to determine the thermodynamics of ligand binding which would support your kinetics data.