Hi there, interesting thread because I have been there, done all that!
I started my masters while childfree and an anal-retentive, type A perfectionist at age 37 and had two babies while doing it. Then I had two more babies.
Yes, four babies, plus masters degree in six and a half years, starting age 37. I'll let you do the math on my fertility. Doing graduate school while pregnant twice in one calendar year was hell. I would not recommend that to my worst enemy... however, it was doable... it's all doable.
I will tell you what, going on this adventure has given me a huge sense of accomplishment. Huge. I feel there is nothing I can't do and nothing my daughters can't do with the right support. I learned more from this experience outside school than in. I had to let go of everything: fear, perfectionism, the concept of the "right" time, and being in control.
The masters has paid off in pay, opportunity, prestige, but most importantly, flexibility for my family. However, I would put family before education. Having children changes perspective and you may find work not as fulfilling once you meet your own baby and realise how challenging motherhood can be.
If I were you, I would accept the paid masters, get a yr of study done, then try for a baby. My university had to hold my spot legally while I went on maternity leave for a year. Look into this.
At the end of the day, however, university will still be open when you're 60, fertility is fickle.
Best wishes!