1.5-card - Ulcanix + any FIRE monster (under Fuwalos)

Requirements:

Whenever you have Ulcanix and a FIRE monster in hand (even if it's Ponix), and your opponent activated Mulcharmy Fuwalos.

This still lets you end on Amblowhale, while giving your opponent just two draws.

Normal Summon Fire King Courtier Ulcanix.
Activate Ulcanix's effect, destroying the FIRE monster in your hand to search Legendary Fire King Ponix.
Activate Ponix's first effect, to Special Summon itself from the hand.
Activate Ponix's second effect, to add Fire King Sanctuary from deck to hand.
Activate Sanctuary, place Fire King Island in the Field Zone.
Activate Island, destroying Ponix for Sacred Fire King Garunix.
Activate Sacred Garunix to Special Summon itself from hand.
Activate Sacred Garunix's second effect to destroy Fire King Avatar Arvata from deck.
- If the FIRE monster you destroyed with Ulcanix was Arvata, destroy Fire King High Avatar Kirin instead.
Activate Arvata/High Kirin after being destroyed by Sacred Garunix, to Special Summon any available Fire King from GY.
Link Summon Promethean Princess, Bestower of Flames using all 3 monsters. (Opponent draws 1 card.)
Activate Princess to Special Summon any FIRE monster from GY.
Link Summon Amphibious Swarmship Amblowhale using Princess and the FIRE monster. (Opponent draws 1 card.)

You should have most of the interruptions from the regular Ulcanix combo.

You do lose out on the Arvata and/or I:P Masquerena though.

The same issues from the main combo apply to this one. Ulcanix, Ponix and Island can be easily negated and will stop your combo.
If you're interrupted and are left with just 2 monsters, check if your opponent has a FIRE monster in their GY. If they do, try to summon Hiita the Fire Charmer, Ablaze and steal it, so you can still make Princess and Amblowhale. Your opponent will draw 3 cards though.