You should consider getting legal advice on this, as the stakes are quite high.
Arriving in the UK later than expected may indeed be a problem: when we moved the UK on Ancestry our immigration lawyer warned us we had to arrive as quickly as possible after the effective date of the visa, so as to avoid the cost of having to extend.
Note that you will need to calculate the days elapsed based on the "effective date" of the visa (when you're allowed to first arrive), not on the "issuance date" (the date the visa was granted in the first place).
The eligibility rule depends exactly how many days you were absent - you mention "3 months", but you will need to be more precise than that to know if you're eligible for ILR or not.
IRL Application Date
It's also worth noting that you you have some leeway about when you apply for the ILR - it may be worth holding off submitting your application until just before it expires.
During the period your ILR application is pending at the Home Office you are allowed to remain in the country: The earliest that you can apply for ILR is 28 days before you're eligible - but the postal ILR application can take 6 months to be approved. So there's a period where your visa could expire, but you're waiting for ILR approval.
You obviously need to be very sure that you have all your documents and paperwork sorted out before doing this!
In the document Indefinite leave to remain: calculating continuous period in UK (page 22) the guidance reads:
Period between the issue of entry clearance and entering the UK
The period between entry clearance being issued and the applicant entering the UK may be counted toward the qualifying period, as long as it does not exceed 90 days. This can occur if the applicant is delayed travelling to the UK.
The period of delay will not be counted as an absence from the UK if it does not exceed 90 days. You must only include whole days in this calculation. Part day absences, for example, less than 24 hours, are not counted. Therefore if the applicant arrived in the UK on day 91, the period would not exceed 90 days.
If the delay is more than 90 days, none of the period between entry clearance being issued and the applicant entering the UK can be included in the continuous period calculation.
According to this ExpatForum post, if the delay was for compassionate reasons you may be able to ask them for further leeway. I've not found reference to this in the guidance, though, so your mileage may vary.
If you've exceeded 90 days, you will unfortunately need to pay for an extension of your Ancestry visa.