There are a few companies out there doing that model, of different sizes (hashicorp, redis labs, wordpress, elastic.co, confluence, etc...). I think it's a good path to take, especially if you already have a robust use base.
Pricing is always the hardest thing because it depends directly on the value that your customers get out of it. If you can, try to find a close competitor and see how much they charge, and start there.
A mentor of mine gave me this advise: If you have customers already asking for support, pick a figure you're comfortable charging (like the 3K you mentioned), double it and start there with one customer. Then, for your next customer, double it again. And repeat until one of your customers pushes back on price. It's incredibly common for developers to undercharge their services, especially to large corporations. If a customer pushes back on the price, you can always offer them a special discount. (note: this only works if you don't publish your prices on your website).
As for what to offer, I would warn against charging a flat fee for building features. I'd develop a standard contract on what support entails (how many hours, how many customer visits, SLA) and negotiate that as a yearly contract. If your customers require a specific feature, I'd negotiate a separate deal.