Sum of Squares reduction test: Convergence criteria met, but not all parameters of the model estimated

Background: I am using weighted non-linear regression to model the growth of plant organs, with dummy variables for different species. I am using a sum of squares reduction test (SSRT) to compare the parameter estimates of the model between the species in my study. For instance, for this logistic equation:

w=(Wo*Wf)/(Wo + (Wf-Wo)*exp(-k*Time))

I want to test if the Wf parameter (asymptotic organ weight) for Species A = Species B, and so on for the rest of the parameters. In my study I have 5 different species, and for a model with 3 parameters, comparing 2 species at a time, I would need 30 SSRTs to make all the relevant comparisons (plus the full model). Here are the SSRT F-tests that I perform to make each comparison (as presented in p.5167 of the SAS 9.3 user's manual):

Fr= ((SSEr-SSEf)/q)/(SSEf/(n-p))

Where SSEr and SSEf are the error sums of squares of the reduced and full models, respectively. q is the number of constraints on the full model to get the reduced model (in my case, setting the values of a parameter equal for two species), n is the number of observations and p is the number of parameters in the full model. I have the code in SAS to do all of this, but I find that in some cases while the convergence criteria is met, SAS cannot estimate all the parameters in the model. Hence, I get that instead of reducing the model by 1 parameter (q=1, since I am making a given parameter equal for two species), I get that the model is actually reduced by 2 or 3 parameters (q=2 or 3). In most (if not all) cases, this makes sense, since some of the species have quite different parameter estimates (e.g. some have very different asymptotic organ weights), and when I make a given parameter equal for two species, I also affect the estimation of the other parameters in the model.

Question: Can I still use these SSRTs that converge, even though I cannot obtain adequate estimates for all the parameters in the reduced models? I am concerned that the SSEr in these situations may not be reliable (and thus, the Ftests), since SAS could not find estimates for all the parameters. Again, I am not interested in the parameter estimates from the SSRTs, I just want to know if the species are different for individual parameters or not.

As an aside, I should mention that I have tried everything from reparameterizing the model, transforming variables/data, different numerical methods, parameter starting values, bounds... and still nothing. I did not change the standard convergence criteria either