I don't know what assumptions were made for that study, but there are lots of ways to get the P/W ratio up (in theory):
1. Fast reactor - no moderator, less bulk, less shielding.
2. Isotopically pure fuel.
3. Only provide shielding on the crew-ward side. Everyone else better stand the fuck back when the reactor is on.
4. Higher temperature operation. An airborne reactor is of course ultimately air cooled, which limits heat wasting; if you operate at the boiling point of plutonium you get about 20x the work/waste ratio (and thus 0.05 as much core for a given airflow) as compared to a commercial power reactor.
5. Direct air cooling of the core, eliminating a lot of pumps, pipes, and heat exchangers.
6. No sissified redundant backup cooling systems or decay heat removal. What, do you want to live forever? We only shut the reactor down at airfields that have cooling water pumps.
7. Molten salt/metal coolant. Low pressure eliminates the need for a massive pressure vessel for the core.
8. On-line purging of xenon from liquid fuel.
9. Sacrificial neutron shielding using using separated isotopes of cadmium and gadolinium?
I bet an aircraft of only a hundred tons could achieve the same P/W ratio as a jet, without counting the fuel weight. And of course, it can fly for years without landing.
EDIT: Looks like solid gold might be a more cost-effective shield for fast neutrons. Even more cooler.