p-value and estimation of parameters with non linear least squares

Hi I am performing an estimation of some parameters . I Have the next data:

Spoiler:

I am using nls.lm() function, and I am trying to fit this data to a logistic distribution.
In order to realize this I have defined the next things in R.

u_x<-datos\$mx (force_of_mortality(x))

A=0.08
k=5
alpha=0.3
gamma=0.27

library(minpack.lm)
######hazard function logistic#####
getPred<-function(p,xdata)p\$gamma+((p\$k*p\$A*exp(p\$alpha*xdata))/1+p\$A*exp(p\$alpha*xdata))
###function to minimize
residFun<-function(p1,observed,xdata)observed-getPred(p1,xdata)
#####Initial parameters
parStart<-list(A=A,k=k,alpha=alpha,gamma=gamma)

summary(nls.out)

Finally I got this Parameters:
Estimate Std. Error t value Pr(>|t|)
A 4.741e-03 1.012e+04 0.000 1.0000
k -1.161e-01 1.886e+06 0.000 1.0000
alpha 4.752e-02 1.844e-02 2.577 0.0125 *
gamma -7.520e-02 9.653e-02 -0.779 0.4391
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

Residual standard error: 0.1972 on 58 degrees of freedom
Number of iterations to termination: 74

I am not sure how to give an accurate interpretation of Pr(>|t|) , in this case I suposse that only the parameter alpha is signficative, then I should to eliminate the other parameters of the model??
In other cases I use another initial parameters, and I got all the parameters significative, i.e every Pr(>|t|) es lower than 0.05. However if I plot with all parameters significative the plot doesn΄t seems well.
For instance I use this initial values:
A=0.021
k=4
alpha=0.299
gamma=0.002
I got this results :
Parameters:
Estimate Std. Error t value Pr(>|t|)
A 1.205e-02 2.027e-07 5.947e+04 < 2e-16 ***
k -1.000e+00 8.584e-14 -1.165e+13 < 2e-16 ***
alpha 2.990e-01 1.058e-05 2.827e+04 < 2e-16 ***
gamma 1.376e-01 3.507e-02 3.923e+00 0.000234 ***

I show both graphs:
plot1.pdf
plot2.pdf

Can you recomend how to give accurate intial values??
And how to proceed with the P values??