Bloodline Familiars
Those with an inherent connection to magic often attract creatures who feel a similar instinctive pull toward magical forces. At 1st level, a sorcerer, bloodrager, or any other character with one of the following bloodlines can choose to gain a bloodline familiar. The character gains a familiar (as a wizard’s familiar), treating her class level as her wizard level for the purposes of this ability. This familiar has an additional ability listed below based on the master’s bloodline.
This replaces the 1st-level bloodline power granted by the character’s bloodline; in addition, the character gains bonus spells from her bloodline one level later than she normally would. For example, a sorcerer with the aberrant bloodline who takes a bloodline familiar would not gain the acidic ray bloodline power, and she would gain her first bonus spell at 4th level, her second bonus spell at 6th level, and so on.
GMs may use the following bloodline familiar abilities as written, or employ them as guidelines for devising bloodline familiar abilities for bloodlines not listed below.
Eldritch Heritage
You are descended from a long line of sorcerers, and some portion of their power flows in your veins.
Prerequisites: Cha 13, Skill Focus with the class skill of bloodline selected for this feat (see below), character level 3rd.
Benefit: Select one sorcerer bloodline. You must have Skill focus in the class skill that bloodline grants to a sorcerer at 1st level (for example, Heal for the celestial bloodline). This bloodline cannot be a bloodline you already have. You gain the first-level bloodline power for the selected bloodline. For purposes of using that power, treat your sorcerer level as equal to your character level – 2, even if you have levels in sorcerer. You do not gain any of the other bloodline abilities.
It's pretty cut and dry. You must take a blood familiar at 1st level. It doesn't say anywhere in there that those taking Eldritch Heritage can select it, and I'm a big fan of "it does what it says and it says what it does." Honestly, if it were meant to work with Eld Heritage, they would have specified as such, and just because it doesn't actually say that it cannot be used with Eldritch Heritage does not necessitate that it can in fact be used by Eld Heritage.
Furthermore, delaying spells is also a requirement. That’s already been covered by Ryan Freire and Gray Warden though. Also furthermore, Eld Heritage doesn’t confer a bloodline upon you, just a latent power from your sorcerer ancestors.
It sounds like it would work if you multi-classed into a Sorc or Bloodrager though. So maybe dip a level in Bloodrager and call it a day. You could always talk to your GM into allowing you to take a bloodline familiar with the Eld Heritage feat, but know that it isn't RAW.
As far as the OP's question: the +6 bonus is an inherent bonus and isn’t achievable until level 17 (or 19 via Imp Eld Heritage), which is the same style of bonus granted by Wish to increase ability scores and you can do this up to a maximum of +5 inherent bonus using Wish. If the +1 str is absolutely pivotal to your build, then yes I believe this is the only way to get a +6 inherent bonus to Str. Otherwise, I'd suggest taking a different bloodline for Eld Heritage (Arcane will give you a familiar) or simply save yourself two feats and not take Eld Heritage at all and boost your inherent str bonus using Wish.
The original character is already sorc 5. I guess if they took a level in bloodrager (restricted to draconic bloodline) they could alter the bloodrager bloodline to get the familiar, but at this point the familiar would be level 1 from a level like 13 character and im not too convinced is really worth it.