I think that Paladin's the better defensive option, and Monk the better offensive one. I've been playing through Beast of Winter since 4.0 went live on beta with a Blood Mage/Paladin, and it's essentially unkillable. Granted, Wizard/Paladins have pretty much always been unkillable, but Blood Mage gives you basically infinite Spirit Shield/Llengrath's Displaced Image/Infuse w Vital Essence/Arcane Veil/etc., along with basically infinite use of the other useful spells in those first three tiers as you need - Chill Fog, Expose Vulnerabilities, Arcane Dampener, Combusting Wounds , Miasma of Dull-Mindedness, etc. Not having to worry about saving up for defensive spells has definitely opened a ton of doors with the Arcane Knight as a utility caster. With Blood Mage regen, Exalted Endurance, and my open spell slots almost always being in the first 3 levels, I've never really even felt the cost of Blood Sacrifice.
Monk would do basically the same thing, but has better synergy as a striker than a meat shield with utility. Eldritch Aim's Aware is the one martial buff a Monk could use but doesn't have (I'd go and adjust the duration up to 15/20s just for QoL), Wizard's Double works perfectly with Dance of Death, DAoM is more free Wounds plus the ability to run away at will if you're in trouble, Merciless Gaze might actually be worth a cast w/ Swift Flurry and infinite spell slots, etc. If you went Helwalker, there are a lot of options to mitigate the downside. If you went Nalpazca, eventually getting Arcane Reflection will give you a great defensive option against that subclasses biggest weakness - enemy casters stripping your beneficial effects (drugs) and causing a drug crash mid battle.
Either way, you're going to be living in that first 3 or 4 spell tiers so I wouldn't recommend multiclassing Blood Mage if you're looking for lots of big spells, because every time you hit one of those fast-cast low tier ones you're just making it less likely to get a big cast back. It would probably be okay single-classed if you focused exclusively on top-tier stuff, but with the way the rest mechanics work in this game I'd rather have no subclass so that I could empower and use my lower level spells at will.