It sounds plausible, depending on the execution. Greece and Rome had societies that included elected officials alongside hereditary/appointed ones, and as France lurched slowly toward democracy, something vaguely like the parliament of nobles/clergy/citizens/etc. you describe existed (it's where we get certain terms we use today, like the use of "left" and "right" to refer to certain political persuasions*), the questions come down to what expectations are placed on the participants and what powers are given to them. E.g. is the Council in effect "actually" in charge, and the Parliament is mostly a rubber-stamp society (e.g. the Roman Senate after Caesar Augustus took power)? Or is it reversed, where a monarch who has a specific vision that conflicts with the dominant power bloc of the Parliament is SOL (e.g. Britain after roughly 1700)? Or is it like the American bicameral system, where certain critical things belong to each house (e.g. revenue bills must start in the House, not the Senate; but the Senate handles essentially all appointment approvals)?
Overall it sounds like you're leaning toward the latter, so if you want it to end up rich, diverse, and competitive, consider how you want to split legislative power between the two branches. I imagine any populist/democratic negotiators at the constitutional committee would be very suspicious of giving too much power to the (almost entirely) unelected Council and would demand some form of oversight to address possible corruption. E.g. in our world, the Catholic Church is probably the largest single landowner in the world (by a huge margin), so your "High Priest of All Gods" has an incredibly powerful position: in theory they can give orders to the clergy in the Parliament and offer financial incentive to other members of the Council, e.g. the Duke and the Senior Guildmaster(s), thus potentially making the whole government subject to the Church's desires (almost) alone (especially with two Senior Guildmasters--as they could bring the guild bloc in Parliament.)
Conversely, no monarch in medieval history ever gladly surrendered their power, and usually required financial or military incentive, e.g. the First Barons' War to force King John to recognize the Magna Carta, or other things where a king was cash-strapped and had to accept greater power/autonomy for their vassals/populace. Even if the King is quite popular with the people when working to set up this new constitutional monarchy, you're going to want to think about why he is willing to share power that previously had been entirely his without oversight. Personally, I'd recommend having a powerful rebellious force of peasants, incensed over the depredations of the former "Crown Prince" (that is, the lich) and demanding concessions to prevent such problems from happening again. The truth of the matter would thus be irrelevant; it doesn't matter that this was a case of stolen identity, it matters that if another King were to go mad-tyrant, they've seen how bad and abusive that could be. Concessions to placate the citizenry after such a severe political crisis are common and would be a reasonable justification for a much more classically-liberal, semi-democratic state.
*Conservatives/traditionalists sat on the National Assembly President's right, while liberals/revolutionaries sat on the President's left. Anyone who didn't fit into either of those categories thus sat in the center.
Short-term pros:
As noted, most NPCs are reusable
Players already know most of the medium-term context, with only a small update to fill in the missing bits
Less work for you, potentially a lot less
Players start off already fairly fully invested in the current dealings
Short-term cons:
Not really much of an update, doubly so if most NPCs are reused
Such early years tend to be full of upheaval as the new system comes into its own
Traditions and norms don't exist yet, so decisions can have much more dramatic consequences than intended
Reused NPCs can be awkward, as there may be strong emotions even though the new PCs shouldn't have any
Long-term pros:
Greater freedom to produce the tone and style you are looking for
Some NPCs are still reusable, if they aren't human, or were relatively young, especially if they're clergy, nobility/royalty, or aristocracy*
Roughly two full generations is long enough for norms/traditions and overall stability to form, showing this government does work
History can still matter! But opinion drifts, maybe driving fun conflict/irony as players know the true events, even as history and people forget
Long-term cons:
More work, as mentioned above. Can't use that extra freedom without effort.
Players have a lot more they need to digest, and essentially have to be re-sold on the setting; "the past is another country" made manifest
Potentially having to explain either how technology/magic has changed the world, or why medieval stasis remains intact
Potentially having to fill up those 50 years with a bunch of historical events, even though some of those events might not matter to the game.
I think that covers most of the core points.
*Keep in mind, kings frequently lived to be 60 or older--even William the Conqueror, who lived in the thirteenth century, died a week after his 59th birthday.
