The Peerless FSL-1830R09-08 would be a nice fit for your door sub. It has a high excursion you usually do not find with drivers this size and price. Do not look at toutlehautparleur.com , it is ridiculous expensive there. Should be more like 150€.
What you also need is a small, bridgeable PA amp and a DSP to match it to your room (you find both at Thomann). Consider the Behringer DCX2496LE Ultradrive and a the t.amp E-800 as a combination. This pair is in the price range of a plate amp, but is higher sound quality, more reliable and much more powerfull. Last it has a very high price on the used market, if you want something new in the future.
A realistic budget for your sub will be 550-700 €.
PS the DSP will not only equalize your sub, but also match your main speakers to the room.
What you also need is a small, bridgeable PA amp and a DSP to match it to your room (you find both at Thomann). Consider the Behringer DCX2496LE Ultradrive and a the t.amp E-800 as a combination. This pair is in the price range of a plate amp, but is higher sound quality, more reliable and much more powerfull. Last it has a very high price on the used market, if you want something new in the future.
A realistic budget for your sub will be 550-700 €.
PS the DSP will not only equalize your sub, but also match your main speakers to the room.