Rollover contributions are not subject to the annual limits that apply to regular contributions. Provided that none of the offset distribution is a Required Minimum Distribution from the 401(k) because you are age 70½ or over in 2019, the entire offset distribution is eligible for rollover.
The 401(k) plan at your old employer was required by law to provide you with an explanation of your rollover options (unless you waived that obligation).
Perhaps you can roll your old 401(k) over to the new employer's 401(k), obtain a loan from the new employer's 401(k) and use the loan proceeds to complete the rollover of the offset distribution. I'm not sure that this loan would qualify for a loan term of more than 5-years, though, because the loan is being used to fund the rollover of the offset distribution, not fund the acquisition of the home.
