Have you tried cleaning out the tunnel and extraction these do get gummed up with flux.

The stains should be a clear residue unless it is white powder and if it is and does not dissolve easily in a common cleaning aerosol then it is mineral salts leaching out of the resist and nothing to do with the reflow oven.

Most oven incorporate some type of flux management system. They are either standard or optional features of an oven. Look to make sure this feature is present and operating correctly to the manual. Heated flux will remaining in the oven environment until they reach a temperature that allow them to condensate.

Typically, if you open your oven and see flux residues they will be attached to the coolest surface. Sound like something is wrong with the oven or not being maintained well, or good enough, most likely the latter of the two.

Paste "staining" ?? Does not sound correct. First check that your thermal profile is with in the manufacture thermal windows and requirements for the paste. This is done by completing a profile of the assembly.

Some residues will remain with most pastes. If you are within the thermal boundaries of the paste specifications and you still would like less residue, consult your paste manufacture. They most likely have a better match for you.

Most people want minimal flux residue left on a circuit board.

This is achieved by volatising as much of the residue as possible during reflow.

Unfortunately the volatised solids will condense at some point on a cooler surface and possibly drip onto your boards.

One way to minimise this is to keep the exhaust as hot as possible for as long as possible to prevent condensation in the oven.

Insulating your exhaust ducting up to a point where it will not allow drip back onto the board is one option.

Modern reflow systems do have the flux management units equipped with cooling units, filters, heat exchangers, filter panels which in production are subject to contaminations such as flux, colophonium.

In order to have these parts operate at maximum efficiency; at certain time intervals, parts need to be removed from the oven and cleaned with a maintenance defluxing agent to remove the flux build up around the parts to increase the heat exchange or filtration process efficiency.

Zestron manufactures such water-based cleaning agent (such as VIGON RC 101 or ATRON SP200) to prolong your equipment's efficiency.