Please confirm my understanding of this bit of redundancy policy

Brie

Ok so going through the documents to ensure I understand what is happening with my current redundancy situation and was surprised by some of this.

You may elect to shorten your Displacement Leave and bring your leaving date forward (this cannot be earlier than the start date of displacement leave advised to you), e.g. if you plan to take up a role with a new employer.  If this is agreed, no payment will be made in lieu of any remaining Displacement  Leave, notice period or untaken holidays including for legacy Banked and purchased holiday, however your redundancy payment will continue to be calculated on your original leaving date. 

Now I quite get that I'm in the office until X and then will have displacement leave when I still get my normal salary but get to sit at home doing diddly.  As doing diddly isn't in my nature I'm already out job searching for my next dream job.  And timing is such that there will be about 6 weeks between an interview and X date when my displacement leave will start.  So potentially I could start a new job with a new employer on the following Monday, without getting to sit about.  I can't find anything in the redundancy FAQs that says that I cannot give notice prior to X but I don't want to be silly and lose a substantial payout.  So do I actually have to wait until X to give my notice?   After all I wouldn't be job searching right now if I wasn't being made redundant but I wonder how this would be looked on legally.  And does the employer have any right to say no?

And if I do start with another employer I quite get that I don't get paid for any displacement leave which would be happening when I'm working elsewhere.  So if I start elsewhere a week after X I would get paid for the 1 week but not any more time.  But my length of service used to calculate my redundancy payout would remain the same whether I have 1 week of displacement leave or 1 month.  Does that seem correct?

Also

For employees  subject to UK income  tax-  please note that should you request to reduce your displacement leave to less than your contractual notice period, or any other circumstances arise which result in your notice period not being served in full,  where appropriate we will deduct income tax and employees’ National Insurance contributions at the appropriate rate from any  part of your redundancy payment which comprises post-employment notice pay

Now I read this to mean that if I would normally need to give 4 weeks notice but on X+1 ask for the notice to be 1 week does that mean I would pay tax & NI on just 3 weeks worth of pay from the redundancy payout or is it on the full whack? 

getmore4less

Not clear what they mean by original leaving date

If on garden leave(displacement leave) it should be the actual termination date.

if given PIILON there should be statutory notice added to work out the redundancy date.

If you have accused unused holiday that is more that the period of displacement they should pay it.