Reconsideration denied, waiting for another one

I asked for a mandatory reconsideration and said I would send more evidence. DWP gave no deadline for the evidence, they said on the phone 'as soon you can'. 6 weeks later when I was about to send the evidence a letter arrived saying that they had waited 1 month for the evidence. Then as they hadn't heard from me they reconsidered the claim using the original evidence and came to the same decision. The letter also says: "if further information is received I will be happy to make a new reconsideration decision". Later on it says "If you disagree with what we decided you can appeal to a tribunal. You must do this within one month of the date of this letter." The date of the letter is 30 June but I didn't receive it until 7th July.

On 7th July I sent the new evidence, with a letter which says:

"thank you for letter of 30th June. It arrived today, just as I was about to send you the new evidence I mentioned in my phone call on 25th May. I was not informed that the DWP would wait no longer than 1 month for the new evidence. I was merely asked in that phone call to send it as soon as I could. (As far as I am aware, the DWP has never published a written timescale for the submission of new evidence for a mandatory reconsideration.)

I regret that it has taken me over 6 weeks to submit new evidence. Because of my conditions I found it an impossibly challenging, complex task. I used to rely on my sister for help with these matters, but she now has quite severe health problems of her own, so her help for me is limited and not always effective. I have had to find a friend to give me some additional help. (He is helping me with this letter.)

In your letter you state that “If further evidence is received I will be happy to make a new reconsideration decision using the new evidence.” The new evidence is appended below, and I would very much like to take you up on your offer of another reconsideration.

However, later in your letter you state that “If you disagree with what we decided. You can appeal to a tribunal. You must do this within one month of the date of this letter.” It seems to me that this contradicts your offer of another reconsideration. Could you please let me know how the process proceeds from here? Do I need to appeal to the tribunal by 30th July, or should I wait for your decision?"

I'm assuming that I won't get a positive reconsideration within the next few days, so I'm going to read the guides and send in an appeal, by Special Delivery on Thursday July 27th.