And really that 10 points adds up. What you were thinking
Exergy (that both Lords had both weapons) would actually be 20 points from the list. That kind of stuff adds up very, very quickly. Its not uncommon to see 100-120 points spent on wargear options that are "worth it" that, taken collectively, aren't worth more than having another scoring unit.
minigun762 is on the money. Some cheap and cheerful Lords with the appropriate Marks would make this possible.
Just slapping things together:
115 pts - Chaos Lord w/ Mark of Nurgle, Bike, Power Axe
115 pts - Chaos Lord w/ Mark of Slaanesh, Bike, Lightning Claw
185 pts - Plague Marines (5) w/ (2) Plasma Gun, Rhino
185 pts - Plague Marines (5) w/ (2) Plasma Gun, Rhino
137 pts - Noise Marines (5) w/ (4) Sonic Blasters and (1) Blastmasters
299 pts - Noise Marines (10) w/ (8) Sonic Blasters and (2) Blastmasters, Rhino
108 pts - Chaos Spawn (3) w/ Mark of Nurgle
170 pts - Heldrake w/ Baleflamer
170 pts - Heldrake w/ Baleflamer
115 pts - Predator w/ Autocannon Turret, Lascannon Sponsons
115 pts - Predator w/ Autocannon Turret, Lascannon Sponsons
1749 Total Points
It is not a completely terrible list though at second glance I'd want to put in a Maulerfiend and would probably drop the 5 man Noise Marines to do it and use the extra points (12 I think) on Wargear on existing units.
So its totally possible to take both. Just keep the buy-in costs low by keeping your Lords low in cost.