Sanity check on an external transformer box.

Hi all,
recently I've been trying to rearrange my system and direct some funds towards upgrading my analog components. Doing so means acquiring a Pro-Ject RPM 9.1 table, a Pro-Ject Speed Box SE and a Pro-Ject Tube Box SE.

While I can not complain of the sound quality of Pro-Ject components, a pressing and constant issue are their flimsy outboard AC wallwart boxes that either introduce hum to the system unless placed on a dedicated line or fail within a matter of weeks.

I've grown tired of moving them around sockets or replacing them, so I thought about having an external transformer box built for the Speed Box and the Tube Box with a custom toroidal transformer. My logic says that seeing the requirements of the two components are 16V/1A AC, I should be able to achieve this with a single toroidal transformer with dual secondaries [one for each component] and a AC power line filter to isolate the transformer.

This box would only house the transformer, the AC filter and two outlets for the aforementioned components, as well as a proper IEC inlet. So, a few questions:

1. Would the above work? Seeing the components require AC, shouldn't a simple transformer be enough?

Here are the specifications for both components:

Tube Box SE
Speed Box SE

2. I can't seem to find a 16V + 16V transformer. Would a 18V + 18V work or should I look for a custom wound one?

Looking forward to getting rid of those pesky AC wallwarts.