Advice on Next Steps after Forever Home Purchase

Don’t get too used to the income you’d be better off going with the increased pension contributions straight away at least rather than doing it later. It’ll be hard to sustain 2 full time jobs with 3 small kids unless the second job is very child friendly (eg a teaching role )
 
Now that home improvement loan is no more, and spouse is back working, this gives cashflow latitude, to increase your Employee Pension, and a higher priority, is to reduce that mortgage, by overpaying within the fixed rate limits.
 
Its the EE + ER combined total, that counts, and 10 % in this case, is low.

In this case, the EE nett cost, of increasing pension from 6 % to 12 %on salary alone, is 5,400 per annum, while 9,000 goes into the pot.

In practical cashflow terms. The nett additional pension cost of 5.4 k annually, is just a little over half the cost, the OP was paying on the now cleared home loan.