I will assume that you are asking for the deadline for there to be an agreement so the deal can come into force at or before the end of the withdrawal period. The last day of the withdrawal period is December 31st 2020.
The main difficulty with ratification arises when the deal is a so-called 'mixed agreement', UK in a Changing Europe describes those agreements as follows:
A mixed agreement refers to an agreement – for example, a trade agreement that also deals with regulatory or investment issues – between the EU and a third country that touches both on powers, or competences, exclusive to the EU and on those exclusive to EU member states. Such agreements must be approved by both the EU and by all member states. In some cases, the approval of member states includes the authorisation by sub-national bodies, such as in the case of Belgium.
Since you're talking about ratification in all EU27 states, it's safe to assume you're talking about a mixed agreement.
To get a sense of the time it will take to get it passed in all the required parliaments in the EU27 member states, we can look at previous trade deals. The UK's Institute for Government estimates that it would take at least a year:
How long could it take the EU to ratify a UK–EU deal?
An EU-only deal could take a couple of months. A mixed agreement is likely to take a year or more. Some recent examples include:
Japan–EU: EU only. Signed July 2019; ratified and entered into force in December 2019.
South Korea–EU: Mixed. Signed October 2010; provisionally applied July 2011; ratified and entered into force in December 2015.
Ukraine–EU: Mixed. Signed June 2014; trade aspects provisionally applied January 2016; ratified and entered into force September 2017.
Canada–EU: Mixed. Signed October 2016; provisionally applied in September 2017; full ratification not yet complete.
To answer your specific question:
Has there been any recent analysis on the constitutional timelines for ratification in all 27 countries?
No, because ratification in all those states will not be complete before the December 31st deadline anyway.
It's not even an interesting deadline, because the agreement can come into force without ratification in all those states. The interesting question would be when the deadline is for all requirements to be met for the agreement to come into force on a provisional basis.
To elaborate on that, the same page by the Institute for Government has the following Q&A:
Could a UK–EU deal come into force in the absence of full ratification?
Yes. The EU could provisionally apply the UK–EU treaty but only after the European Parliament and Council have voted on it. This would need to happen by 11pm on 31 December 2020.
Member states could, however, demand that provisional application excludes areas of shared competence. In the case of the Canada–EU Comprehensive Economic and Trade Agreement (CETA), signed in 2016, the vast majority of provisions have to date been provisionally applied in the absence of full ratification. But provisional application excluded some provisions such as those on investment protection. These will only come into force once the deal has been fully ratified by all 27 member states.
As for the deadline on the EU Parliament and EU Council voting on a deal so that it can be applied provisionally, I am not sure. As you said, if there is something to be voted on, I don't see why they wouldn't hold an extraordinary session (they've expressed such intention before in the Brexit saga) to try to get it passed before the deadline.