Chimney too close to roof

Without knowing what you consider "economical", there's no real way to answer the question. Is this a brick chimney? Metal? If brick, have you checked with a mason to find out what it would cost to extend it?

Too close for what?

Does water drain into the chimney when it rains? Are you afraid sparks will ignite the roof? Does it look too ugly?

What's the problem?

You said stove so I'll make the big assumption that its a pipe chimney. Can't you in this case simply re-route the pipe to somewhere more convienent?

Let's hope it's not single-wall smokepipe, but a real chimney of some sort. And that the OP will work on word-pictures.

For one thing a chimney that "butts right up against" "the higher roof" says to me that some sort of roof overhang is above the chimney discharge, which would be really stupid. IMHO.

How long has it been this way? How many times has wood been burned in the stove? How long does each fire last? Has it ever caused a fire, or other problems, or does it just look ugly?

There are building codes about this. I believe, around here, distance to the higher roof must be over 10 feet. If you put in stove and have low pipe, maybe you can extend it. If you paid someone to do it, they should have known better and owe you a repair. Frank

Check local code compliance in your area with the AHJ. If typical, it will require a minimum of 2 feet above the ridge or a minimum of 10 feet from the closest roof surface.

Post a photo !!!

There's a house nearby me that has a brick chimney that ends UNDER the roof overhang. In other words, they built the overhang right over the top of the chimney. I often look at that thing and laugh. I assume it's and unused chimney but it looks rediculous. If by chance it;s is ever used, they can kiss the house goodbye.