Any point in filing a DJP once both owners deceased?

Please can you help clarify the following?

Situation: couple owned their home as joint tenants.  One died a few years ago.  The survivor did not file a DJP.  The survivor passed away a few weeks ago.  Both names are on the Register.

Questions:

a) can a DJP still be filed to remove the name of the first deceased?  Or any other alternative to Form DJP?  A reason for this would be to have a clean, simple title on the Register for marketing purposes. (I understand that a potential new owner can still register title with Death Certificate of first deceased + Probate for the second + Form TR1.  However, it might? make matters simpler if there is no confusion about title when marketing & title searches are done.)

b) assuming a DJP can still be filed to vacate the name of the first deceased, can that now only be done by the executor of the 2nd deceased?

c) if the answer to (b) is yes, can the Registry entertain & process such an application prior to grant of Probate for the estate of the second deceased. (Probate has not yet been applied for.)

d)  how long is it currently taking at the Land Registry to process a DJP/alternative Form to vacate a name?

e) is there any bar to marketing a title/property prior to grant of Probate?

Many thanks.

W Venn - a) form DJP can be used at any time to update the register re a registered owner's death. A death is sadly factual and can be proven at any time but I understand what you are suggesting re doing so making it 'simpler' for example re a probate sale. 
b) Anyone can apply - the death is after all factual and provable
c) Yes
d) it's likely to wait several months before being processed. 
e) there is no bar that I am aware of re marketing the property prior to probate being granted - the estate agent, if used, may have specific requirements re the death of both registered owners but that can vary in my experience

Thank you very much Adam.

- if a DJP is filed now, the property marketed & Probate applied/obtained, would the fact that a DJP is already the pipeline (and possibly take several months to process) then end up complicating a potentially earlier attempt to register a title transfer a few months down the line via the route of filing the Death Certificate (1st deceased) + Probate (2nd deceased) + TRI?

- then, looking at the DJP form and in the light of guidance, I'm perplexed by what it says in a side note on page 2 (by No. 7):  'Please remember that this form is only to be used where there are remaining/surviving registered proprietor(s)'.  

Thank you.

W Venn - no reason why it should complicate matters. 
I can appreciate why you might be perplexed but think of it in terms of the fact that the register does refer to two registered owners. We are unaware that both have died so using the form DJP in the way you propose is acceptable.

If it helps, and based solely on my experience of dealing with similar enquiries over many years, there is rarely a need to do as you are suggesting. Probate for the second deceased owner is the key next stage re actually 'dealing' with the property as in selling it. 
You can prove anyone interested in the facts with a copy of both death certificates and the register. That confirms the legal ownership and their respective deaths. Probate is the important piece of the legal/conveyancing jigsaw as without that nothing fits re the 'executor's' legal ability to sell the property 
It reads as if you are trying to think of ways to make it as simple as possible to explain to someone else that the sale is legitimate as both owners have died and it's a probate sale. The simple way of explaining the former is with a copy of the death certificates and register. The latter becomes simple to explain only once probate is obtained.
As such there appears to be little point in updating the register re the deaths at this stage but you can if you wish to 
Hope that helps