Well you certainly can’t take this as unbiased advice, since I’m CEO of a software vendor that specializes in non-profits, but I do think we have a product that might be just what you are looking for.

Our two primary donor management products are DonorPerfect and DonorPerfect Online. We’ve always worked with relatively small non-profits, but a couple of years ago we began offering an very low-cost option of small nonprofits:
http://www.donorperfect.com/gosales

You can just sign-up for a no risk trial but let me speak to DonorPerfect Online in terms of your requirements:

MUST HAVES
Web-based
Supports multi-users
Provides giving history (as well as giving summaries by year)
Provides extensive reporting
Allows recording of restricted and designated gifts
Provides export of data

NICE TO HAVES
Supports identifying gifts by campaign (as well as solicitation method)
Variety of reports and tools to target solicitations
Option for accepting online donations – fully integrated
Alerts and to dos are part of the systems contact management features

Two things your story mentioned that you didn’t directly address in your requirements list are:

Story 1 – When you enter a gift, DonorPerfect Online lets you specify which thank you letter you want to generate. You could setup a thank you letter that specifically notes that the gift was an increased level of support and how valuable that is to your organization.

Story 2 – Making the connection between various donors can be critical for major donor development.. Doing this requires the ability to establish links between donor records. You can then generate the type of report that could tell you that Donor A shares a relationship directly (or indirectly by a common connection such as an employer) with Donor B.

Hope that helps! By the way, we also provide software for camp management (www.ezcamp2.com).