Application for UK Visa rejected. How do I make my second application stronger? [duplicate]

I am a recent college graduate planning on a graduation trip to London and Scotland.

My tourist visa application was refused because of lack of evidence of my employment and evidence that I will be coming back to my country. Also because of a sudden uplift in my funds, they don’t believe my bank statement is a true reflection of my financial circumstance and that the funds in my bank statement might not be available for my exclusive use.

I believe I have sent an employment letter but no pay slip for the past 6 months. I’ve been working part time at my workplace for the past year and a half. Because I work part time, I do not have a fixed schedule. I work whenever I am free and sometimes it’s only once a month or even not at all because of school commitments so my income might not have been reflected in my 6-month bank statement. I had my finals mid this year as well as my graduation in September so I was only able to cover about 2 shifts at work over the last 6 months and wasn’t able to provide a pay slip.

However I was working more frequently from May to November 2016 and saved my income as well as pocket money from my parents, which amounted to about $4000. I transferred most of my income and deposited my cash allowances to someone else’s account for safekeeping as it was my plan to go on a graduation trip at the end of 2017 and didn’t want to risk spending the money. I only asked to transfer the money back to me before submitting my documents for my visa application. This explains the sudden uplift in my funds. I do see how it looks dodgy and would like to know how I can explain this to them? Would it help if I could provide payslips from 2016 that shows I was indeed getting an income that could amount to $4000?

My father has also offered to do a partial sponsorship of $3000 for my UK trip. He initially intended for the $3000 to be a surprise graduation gift, to be given before I leave for London. However since my visa rejection, he offered to write a letter declaring his role in sponsoring my funds. What should the letter contain and should there be any other documents to support this? Would this help in convincing them that I can in fact, support myself for the 17 days in UK?

As for evidence of return to my country, I am also on a Tuition Grant Scheme with the Government of Singapore which requires me to work in Singapore for 3 years upon graduation, which happened on the 3rd of September 2017. Failure to do so would make me liable for liquidated damages. I did not add this info/document as I wasn’t sure it was necessary. Would this additional info help my case? I also have a return ticket, fully paid!

Please advice on how I can make my application stronger. I am supposed to leave for London on November 30 2017 and have less than 2 weeks to get a visa. I will be travelling with a Friend who has also recently graduated.