A battlemind doesn't have lots of options in that regard, but there are a few with which you may be able to get close to what you want.

Note that other than your suggestion I haven't found a way to significantly increase the range at which a battlemind can mark, so most suggestions here are just workarounds or ideas which could help with increased mobility and so on.

The highest range I could find among battlemind powers with a quick Compendium search was melee weapon +3 reach (Dimensional Ambush^[DDI]) respectively close blast 3 (Obsidian Shield^[DDI]) - the rest was at most close burst 2.

Class features, powers and feats:

• Wild Focus^[DDI]: Battlemind class feature; free action, encounter, close burst 10; pull target Cha modifier squares and mark it till EOYNT.
• Speed of Thought^[DDI]: Battlemind class feature; free action, encounter; move 3 + Cha modifier squares, can be used even when surprised. Can be enhanced to 5 + Cha modifier squares with Improved Speed of Thought^[DDI].
• Persistent Harrier^[DDI]: Battlemind class feature; immediate reaction, encounter, melee weapon; when enemy hits or misses you, you attack him back (even if the target is outside your melee reach) and teleport adjacent to it.
• Iron Trap^[DDI]: Githzerai racial feat; when enemy misses you because of Iron Mind racial feature, the enemy is marked and you gain combat advantage until EOYNT.
• Demand's Reach^[DDI]: Battlemind feat, paragon tier; increase Battlemind's Demand to close burst 5.

Equipment:

• Predatory Weapon^[DDI]: Weapon power; free action, encounter; when hitting with the weapon mark one target within 5 quares until EOYNT.
• Farslayer Weapon^[DDI]: Weapon power; standard action, at-will; make melee basic attack up to 5 squares away.
• Greater Dancing Weapon^[DDI]: Weapon power; minor action, at-will; animate weapon (direct with move action, fly speed 6, must see target squares), while you can see the weapon you can make melee weapon attacks through it (counting the weapon's square as origin square instead of your square).
• Blade of the Eldritch Knight^[DDI]: Weapon property; when using a standard action to make a melee attack increase reach to 5 for that attack.
• Planesplitter Weapon^[DDI]: Weapon power; free action, encounter; when making a melee attack increase weapon reach by +2 squares.

In any case you might want to take a look at the "Beyond Bodily Brutality: the Basics of Building Battleminds" handbook on the WotC boards.

And yes, your assumption is correct. Taking Student of the Sword^[DDI] would allow you to mark any enemy once per encounter with any attack that is made with the selected weapon type (one-handed melee or two-handed melee) regardless of hit or miss.

How to use wild shape

The creature takes a standard action that doesn't provoke attacks of opportunity to use the supernatural ability wild shape. Then you make a new character sheet.

From wild shape, the druid...

• loses the ability to speak if an animal form is assumed, but while in the assumed animal form the druid can make noises and gesticulate like a typical creature of the assumed form.
• gains the ability to communicate with other animals of the same general grouping. Note: Ask the DM what a general grouping is for the assumed form. (That is, do tigers speak the same language as house cats?)

From the effect of a supernatural ability duplicating the effect of the spell beast shape I, the druid...

• gains the base land speed of the assumed form.
• gains a climb speed equal to the assumed form's climb speed but not more than 30 ft.
• gains a fly speed equal to the assumed form's fly speed but not more than 30 ft. This fly speed always has average maneuverability.
• gains a swim speed equal to the assumed form's swim speed but not more than 30 ft. The druid also gains the ability to breathe underwater while swimming.
• gains darkvision with a range equal to the range of the assumed form's darkvision but not more than 60 ft.
• gains low-light vision if the assumed form also has low-light vision.
• gains scent if the assumed form also has scent.
• gains bonuses based on the assumed form's size. Assuming the form of a Small animal grants the druid a +2 size bonus to Dexterity and a +1 natural armor bonus. Assuming the form of a Medium animal grants the druid a +2 size bonus to Strength and a +2 natural armor bonus.

From the effect of a supernatural ability duplicating the effect of a spell of the transmutation subschool polymorph, the druid...

• gains the natural attacks of the assumed form and proficiency sufficient to use those attacks. Note: The druid uses his own base attack bonus but his modified ability scores to determine attack bonus and final damage with these natural attacks.
• gains a +10 bonus on Disguise skill checks made to masquerade as an animal of the assumed form, although specific creatures' forms can't be assumed.
• gains the appropriate size modifiers to armor class and on his attack bonus, Combat Maneuver Bonus, and Stealth skill checks if the druid has changed size. Note: This should also likely include modifiers to Fly skill checks, but this goes unmentioned by the text.
• sees all his carried gear meld into his new form because the assumed form is that of an animal (or plant or elemental). The only magic items that continue functioning are those that both provide constant bonuses and do not need to be activated to function (see here). Note: Enhancement bonuses from magic armor and shields don't usually work either.
• loses the ability to cast spells because the assumed form is that of an animal (or, probably, a plant). Note: The feats Eschew Material and Natural Spell help a druid cast spells while in an assumed form that normally prohibits casting.
• loses extraordinary and supernatural abilities dependent upon on his original form, including keen senses, scent, darkvision, natural attacks, and movement modes.
• loses class features dependent upon his original form, but those class features that allow adding features to the original form can still be used to add such features to the new form. Note: Special restrictions apply to effects of the polymorph subschool (see below).
• gains immunity to other effects of the polymorph subschool. The druid can allow himself to be affected a new polymorph subschool effect, but such an allowance ends this current polymorph subschool effect. Note: This is actually a bigger deal than you might expect.
• gains immunity to effects that change his size.
• gains and loses whatever the GM says he gains and loses if there are any questions. Note: That's actually in the rules.

When the druid gains the ability to also use, for example, beast shape II, the second section is, I think, the only part that needs changing.

Nothing else changes, but the druid's Dexterity-based or Strength-based stuff will need to be adjusted for his modified ability scores. Specifically, a creature that uses the special ability wild shape does not gain the assumed form's skills, does not gain the assumed form's size-based modifiers as if it were advancing as a monster (instead using the special polymorph subschool size change rules), and does not gain the assumed form's base attack bonus nor the assumed form's saving throw bonuses (although the druid's attack bonus and saving throw bonuses may change due to the modified ability scores).