I looked briefly at Lundahl; seems like a good company after a very quick look. Been in business a long time, some good technical info on the site, maybe the European version of Jensen? The SE-Differential converters on the pro audio page look reasonable. I did not dig into the datasheets; you might want to ask them (and Jensen) about your application since source and load impedances are on the high side.
One thing to double-check is XLR polarity; some reverse pins 2 (+) and 3 (-).
As for the REI amp, does the company have suggestions for driving from a SE source? The conventional schemes off-the-cuff are:
1. RCA shield to XLR pin 1 (ground/shield), RCA center to XLR pin 2, XLR pin 3 open;
2. RCA shield to XLR pin 1 (ground/shield), RCA center to XLR pin 2, XLR pin 3 to ground/shield;
3. RCA shield to XLR pin 1 (ground/shield), RCA center to XLR pin 2, XLR pin 3 to ground through a resistor equal to the source impedance (1k in your case, this helps maintain common-mode rejection);
4. Some recommend connecting RCA shield to XLR pin 3 so the XLR shield only goes to the chassis, or to the shield of a balanced cable, perhaps through a resistor;
5. RCA to an active (typically op-amp) or passive (transformer) SE to differential converter to the XLR.
The best connection is usually a converter, but many manufacturers have to deal with SE to differential (and/or balanced) conversion. What works best depends upon the amplifier's internal circuit, the input circuit and grounding scheme, so they should hopefully have suggestions. I only saw balanced from preamp to amp in their user manual, however.