Including resume headers and footers is an aspect of resume-building on which many sources disagree. On one hand, including headers and footers can help job seekers who may have resumes of more than one page in length. However, due to variations in software use from company to company, many resume headers and footers can be lost in translation.
While job seekers who have longer resumes may be tempted to use Word's header/footer feature, these resume parts are not always ideal.
If an applicant has a resume that is more than one page in length, and they are sending the resume electronically through email, including a header or footer that provides information about the applicant so that pages are not lost is a good idea. Providing your information (name, address, contact information, email address, etc) in the header is essential for those who have more than one page to their resume. Adding the word "continued" in the footer and the applicant's last name is a great way to connect the pages of a longer resume.
However, it is important to remember that the software used to create certain resume parts (MSWord, Open Office, etc) may not translate into other programs. For example, if an applicant creates a resume with headers and footers in Microsoft Word and the company receiving the document uses another program, the ability to read resume headers and footers may not be available in the company's software, thus important information connecting pages may not appear, and pages could be lost in the process. This may leave the employer with a sense of an incomplete resume, costing the applicant the chance at an interview.
It may serve the applicant better to simply add a line after the last item on the page and include their last name, and the word "continued" to show employers that there is more than one page. On the following page, the applicant should add the last name again at the top so that employer's can connect the two.
Though resume formats vary from person to person depending on taste, most applicants find that a one-page resume eliminates the need for resume headers and footers. All applicant information is included in the heading of a one-page resume, and potential employers only have to read and print one page. If applicants really want to include resume headers and footers, it may be a good idea for the attached email or letter to mention the number of pages so that employers are aware.
While applicants who have a longer resume may find benefits in using resume headers and footers, it is not necessarily an ideal way to connect pages of a longer resume. Resume headers and footers are not necessary at all within resumes that are only one page in length given that all applicant information is in the heading of the resume.
("Resume Design" by CharlotWest licensed by CC BY-SA 2.0)
This satisfies some of your desiderata. In particular, it uses the footer on all pages.
I'm not certain how exactly you want the footer moved up without changing the bottom margin. If 'bottom margin' is intended to include the footer, obviously you cannot move the footer up without changing it. So I assume you mean 'bottom margin' as the bottom of the last line of the body of the letter on the page. But then I don't see how the footer can move up without changing the margin. Not, at least, without making things look awful. So I've not attempted this here.
Finally, having taken a look at the code of the class, personally I would learn to live with the colons. However, you may feel differently if you dislike them strongly enough. (The documented code is not included in the manual I have and the code itself contains precious little by way of commentary. Eventually, I gave up trying to figure out which command might be responsible for the colons. However, I suspect it is buried fairly deep so that you would have to duplicate a fair chunk of code in your preamble. Obviously that's doable but I would not personally think it worth it. I could, however, been entirely misguided in my suspicions.)
So, in the end, I've only really changed one thing: