lme4/lmer: P-Values from mcmc samples or chi2-tests?

Dear R users,

I have now tried out several options of obtaining p-values for 
(quasi)poisson lmer models, including Markov-chain Monte Carlo sampling 
and single-term deletions with subsequent chi-square tests (although I 
am aware that the latter may be problematic).

However, I encountered several problems that can be classified as
(1) the quasipoisson lmer model does not give p-values when summary() is 
called (see below)
(2) dependence on the size of the mcmc sample
(3) lack of correspondence between different p-value estimates.

How can I proceed, left with these uncertainties in the estimations of 
the p-values?

Below is the corresponding R code with some output so that you can see 
it all for your own:

##
m1<-lmer(number_pollinators~logpatch+loghab+landscape_diversity+(1|site),primula,poisson,method="ML")
m2<-lmer(number_pollinators~logpatch+loghab+landscape_diversity+(1|site),primula,quasipoisson,method="ML")
summary(m1);summary(m2)

#m1: [...]
Fixed effects:
                     Estimate Std. Error z value Pr(>|z|)
(Intercept)         -0.40302    0.57403 -0.7021  0.48262
logpatch             0.10915    0.04111  2.6552  0.00793 **
loghab               0.08750    0.06128  1.4279  0.15331
landscape_diversity  1.02338    0.40604  2.5204  0.01172 *

The p-values from mcmc are:

##
markov1=mcmcsamp(m2,5000)

HPDinterval(markov1)
                             lower      upper
(Intercept)          -1.394287660  0.6023229
logpatch              0.031154910  0.1906861
loghab                0.002961281  0.2165285
landscape_diversity   0.245623183  1.6442544
log(site.(In))      -41.156007604 -1.6993996
attr(,"Probability")
[1] 0.95

##

mcmcpvalue(as.matrix(markov1[,1])) #i.e. the p value for the intercept
[1] 0.3668

 > mcmcpvalue(as.matrix(markov1[,2])) #i.e. the p-value for logpatch

[1] 0.004

 > mcmcpvalue(as.matrix(markov1[,3])) #i.e. the p-value for loghab

[1] 0.0598

 > mcmcpvalue(as.matrix(markov1[,4])) #i.e. the p-value for landscape.div

[1] 0.0074

If one runs the mcmcsamp function for, say, 50,000 runs, the p-values 
are slightly different (not shown here).

##here are the p-values summarized in tabular form:

logpatch         	0.004
loghab            	0.0598
landscape_diversity    	0.0074

logpatch        	0.007106
loghab            	0.1704
landscape_diversity    	0.01276

To summarize, at least for quasipoisson models, the p-values obtained 
from mcmcpvalue() are quite different from those obtained using 
single-term deletions followed by a chisquare test.

Especially in the case of "loghab", the difference is so huge that one 
could tend to interpret one of the p-values as "marginally significant".