Would I have enough power?

My answer is "no".

It's not the tube, nor the power. It's the 88dB speakers.

No. That 'room' and that efficiency won't get it.

It depends on the size of the room.  In smaller room, when distance to speaker is about 2m (6.6ft), it should be OK.  At 15 watt it will be around 100dB - pretty loud.  

@greg7,
Kijanki makes a key point/observation. The 88db sensitivity will impact maximum volume capability and required amplifier power to do so. You listen at "moderate levels" so there’s less demand for power. If by modest levels you mean 65 to 80 db at C-weighted SPL you’d only be using a couple of watts at most.

Listening in the sub 75 db range, definitely less than a watt would be utilized. Get a SPL meter to confirm your actual typical listening levels.
Based on your provided specs, these speakers with a minimum 8 ohm impedance (And simple crossover) are an easily driven load. In my opinion a 10 to 15 watt tube amplifier with quality power supply and output transformers should be fine for your intended use.

If you were to need the ability to play music frequently at louder SPL (95-105 db) sitting 9 feet away I’d recommend more power. However for your stated goal/ desires I believe tube amplifier watt quality is the priority. An example, numerous listeners have been happy driving Rogers BBC LS3/5A monitors (83-84 db 16 ohm impedance) with lower watt tube amplifiers. These types of listeners were only interested in moderate volume in their listening space.
Charles