Is it possible to speed up a forced dialogue?

Nearly all of these dialogs are tied to a quest. In most cases, it's reasonably safe to use setstage to skip to the next stage of the quest, which effectively skips the dialog. However, you should always make a full, numbered save before using the console for this or any other purpose. Keep that save at least until you have entirely completed the offending quest, just in case it's broken. Here's the usual process:

0. If you have already started the dialog, it's too late. Load an earlier save, or just suffer through it.
1. Find the quest in UESP. Let's use The Only Cure as an example (to skip Peryite's dialog).
2. Scroll to the bottom of the page. There will be a table marked "Quest Stages". The table's main header will contain the name of the quest along with its ID. If there are multiple quests, then you will see multiple headers. In the case of The Only Cure, the quest ID is DA13.
3. Look through the table to identify your current journal entry and quest objective, then use setstage to skip ahead to the next row in the table. In the case of a quest with multiple choices, you will need to correctly identify which stage comes after the current stage, depending on the choice you made (see for example Ill Met By Moonlight, which has stages 100 and 105 representing different possible outcomes of the quest). For our example, you would look at your journal, which says "There is a fuming incense..." and directs you to inhale said incense (in order to converse with Peryite). Comparing this to the table, we're currently on stage 21, and we need to get to stage 40. You would run setstage DA13 40. Capitalization does not matter.
4. If the quest-giver was supposed to provide you with some sort of item or reward, check your inventory. If you don't have it, load your save and just do the quest the normal way.